Mitochondrial Eve
Mitochondrial Eve (mt-mrca) is the name given by researchers to the woman who is defined as the matrilineal most recent common ancestor (MRCA) for all living humans. Passed down from mothers to offspring for over a hundred thousand years, her mitochondrial DNA (mtDNA) is now found in all living humans: every mtDNA in every living person is derived from hers. Mitochondrial Eve is the female counterpart of  Y-chromosomal Adam, the patrilineal most recent common ancestor, although they lived at different times.
She is believed to have lived  about 140,000 years ago in what is now Ethiopia, Kenya or Tanzania.  The time she lived is calculated based on the molecular clock technique of correlating elapsed time with observed genetic drift.
Mitochondrial Eve is the most recent common ancestor (MRCA) of all humans via the mitochondrial DNA pathway, not the unqualified MRCA of all humanity.  All living humans can trace their ancestry back to the MRCA via at least one of their parents, but Mitochondrial Eve can only be reached via the maternal line.  Therefore, she necessarily lived much longer ago than the MRCA of all humanity.
The existence of Mitochondrial Eve and Y-chromosomal Adam does not imply the existence of population bottlenecks or a first couple. They each lived within a large human population at a different time.  Some of their contemporaries have no living descendants today, and others are ancestors of all people alive today.  No contemporary of Mitochondrial Eve or Y-chromosomal Adam is an ancestor of only a subset of people alive today, because both of them lived much longer ago than the identical ancestors point.

# Matrilineal descent
Mitochondrial Eve is the most recent common ancestor of all humans via the mitochondrial DNA pathway. In other words, she is the MRCA found when ancestry of all living humans is traced back in time, following only the maternal lineage.  The mitochondrial DNA pathway is equivalent to maternal lineage, because Mitochondrial DNA is only passed down from mother to child, never father to child.
To find the Mitochondrial Eve of all humans living today, one can start by listing all individuals alive today.  For every individual (males and females), trace a line from the individual to his/her mother.  Then continue those lines from each of those mothers to their mothers, and so on, effectively tracing a family tree backward in time based purely on mitochondrial lineages.  Going back through time these mitochondrial lineages will converge when two or more women have the same mother.  The further back in time one goes, the fewer mitochondrial ancestors of living humans there will be, until only one is left. This is the most recent common matrilineal ancestor of all humans alive today, i.e. Mitochondrial Eve.
It is possible to draw the same matrilineal tree forward in time by starting with all contemporary human females of Mitochondrial Eve.  Some of these women may have died childless.  Others left only male children.  For the rest who became mothers with at least one daughter, one can trace a line forward in time connecting them to their daughters.  As the forward lineages progress in time, more and more lineage lines become extinct, because the last female in the line dies childless or left no female children.  Eventually, only one single lineage remains, which includes all mothers, and in the next generation, all people, and hence all people alive today.

# Misconceptions
Mitochondrial Eve is the most recent common matrilineal ancestor, not the most recent common ancestor (MRCA) of all humans.  The MRCA's offspring have led to all living humans via sons and daughters, but Mitochondrial Eve must be traced only through female lineages, so she is estimated to have lived much longer ago than the MRCA.  While Mitochondrial Eve is thought to have been living around 140,000 years ago, according to probabilistic studies, the MRCA could have been living as recently as 3,000 years ago.
Allan Wilson's naming Mitochondrial Eve after Eve of the Genesis creation story has led to some misunderstandings among the general public. A common misconception is that Mitochondrial Eve was the only living human female of her time  she was not. Had she been the only living female of her time, humanity would most likely have become extinct due to an extreme population bottleneck.
Indeed, not only were many women alive at the same time as Mitochondrial Eve but many of them have descendants alive today.  They may have left descendants via either son or daughters (and grandsons or granddaughters, and so on). Nuclear genes from these contemporary women of Mitochondrial Eve may be present in today's population, but mitochondrial DNA from them is not.
What distinguishes Mitochondrial Eve (and her matrilineal ancestors) from all her female contemporaries is that she has a purely matrilineal line of descent to all humans alive today, whereas all her contemporaries have at least one male in every line of descent. Because mitochondrial DNA is only passed through matrilineal descent, all humans alive today have mitochondrial DNA that is traceable back to Mitochondrial Eve.
Furthermore, it can be shown that every contemporary woman of Mitochondrial Eve either has no living descendant today or is an ancestor to all living people. Starting with 'the' MRCA at around 3,000 years ago, one can trace all ancestors of the MRCA backward in time.  At every ancestral generation, more and more ancestors (via both paternal and maternal lines) of MRCA are found. These ancestors are by definition also common ancestors of all living people. Eventually, there will be a point in past where all humans can be divided into two groups: those who left no descendants today and those who are common ancestors of all living humans today. This point in time is termed the identical ancestors point and is estimated to be between 5,000 and 15,000 years ago. Since Mitochondrial Eve  is estimated to have lived more than hundred thousand years before the identical ancestors point, every woman contemporary to her is either not an ancestor of any living people, or a common ancestor of all living people.

# Mitochondrial DNA
We know about Eve because of mitochondrial organelles that are passed only from mother to offspring.  (Strictly speaking, the sperm do bring some mitochondria to the egg, but their contribution amounts to at most about 0.01% of the fertilized egg's total, so is normally ignored.)  Each mitochondrion contains Mitochondrial DNA (mtDNA). A comparison of DNA sequences from mtDNA in a population reveals a molecular phylogeny.  Unlike mtDNA outside the nucleus, genes in nuclear DNA become recombined after being inherited from both parents, and therefore we can be statistically less certain about nuclear DNA origins than we can for mtDNA, which is only inherited from the mother.  mtDNA also mutates at a higher rate compared to nuclear DNA, so it gives researchers a more useful, magnified view of the diversity present in a population.
Just as mitochondria are inherited matrilineally, Y-chromosomes are inherited patrilineally.  Thus it is possible to apply the same principles outlined above to men.  The common patrilineal ancestor of all humans alive today has been dubbed Y-chromosomal Adam.  Importantly, the genetic evidence suggests that the most recent patriarch of all humanity is much more recent than the most recent matriarch, suggesting that 'Adam' and 'Eve' were not alive at the same time. While 'Eve' is believed to be alive 140,000 years ago, 'Adam' lived only 60,000 years ago.

# Eve and the Out-of-Africa theory
Since Mitochondrial Eve is believed to have lived in Africa she is sometimes referred to as African Eve, an ancestor who has been hypothesized on the grounds of fossil as well as DNA evidence. According to the most common interpretation of the mitochondrial DNA data, the titles belong to the same hypothetical woman. Family trees (or "phylogenies") constructed on the basis of mitochondrial DNA comparisons show that the living humans whose mitochondrial lineages branched earliest from the tree are indigenous Africans, whereas the lineages of indigenous peoples on other continents all branch off from African lines. Researchers therefore reason that all living humans descend from Africans, some of whom migrated out of Africa and populated the rest of the world. If the mitochondrial analysis is correct, then because mitochondrial Eve represents the root of the mitochondrial family tree, she must have predated the exodus and lived in Africa. Therefore many researchers take the mitochondrial evidence as support for the "single-origin" or Out-of-Africa model.
Some people use the mtDNA family tree as evidence of a population bottleneck (e.g. Toba catastrophe theory) giving rise to the human species.  There are, however, many ways such family trees can be constructed.  A tree can be constructed based on any gene, not just the mitochondrial DNA.  When different such trees including the mtDNA tree are compared, no population bottleneck is found because different trees show different coalescent points.  The inconsistencies between coalescent points indicate that there had been numerous gene interchanges between population groups around the world, even after the first exodus out of Africa.  This idea forms the basis of Alan Templeton's 'Out of Africa Again and Again' theory.
The Mitochondrial DNA provides another support for the Out of Africa hypothesis in the form of gene diversity. One finding not subject to interpretation is that the greatest diversity of mitochondrial DNA sequences exists among Africans. This diversity is widely believed to have  accumulated because humans have been living longer in Africa than anywhere, although the same relative diversity can also be explained if just more people lived in Africa than in other regions - an interpretation of the past that all evolutionary models also accept, even those that contradict the African-origin theory, such as Multiregional evolution.

# Academic investigation
Criticisms of the original paper by Cann, Stoneking and Wilson include:
- Of the 147 persons sampled, only two were from sub-Saharan Africa. The other 18 'Africans' in the study were African-Americans.
- The method to generate the tree was not guaranteed to find the most parsimonious tree.
- The method used to root the tree placed it at the midpoint of the longest branch (midpoint rooting). This could lead to a wrong position of the root if for example the rate of evolution is higher in Africa.
- Restriction-fragment length polymorphism is ill-suited for estimation of mutation rates which is essential in timing evolutionary events.
- Weak statistical analysis.
Ingman et al. (2000) repeated the study while avoiding its major pitfalls:
- They sampled 53 persons, 32 of whom were Africans from different regions of sub-Saharan Africa.
- They sequenced the complete mtDNA but excluded the rapidly evolving D-loop in the analysis.
- An outgroup (chimpanzee) mtDNA sequence was used to root the tree (outgroup rooting). Outgroup rooting is much more reliable than midpoint rooting.
The study by Ingman et al. verifies the major conclusions of Cann et al. of an African origin of human mtDNA within the past 172 000  50 000 years.

# In popular culture
- Bryan Sykes has written a popular science book entitled The Seven Daughters of Eve.
- In River Out of Eden, Richard Dawkins discusses human ancestry in the context of a river of genes and shows that Mitochondrial Eve is one of the many common ancestors we can trace back to via different gene pathways.
- The Discovery Channel has produced a documentary entitled The Real Eve, based on the book Out of Eden by Stephen Oppenheimer.
- The Japanese novel, horror film and video game series Parasite Eve uses the Mitochondrial Eve theory as the basis for a fantasy about a scientist resurrecting his wife by regenerating her liver cells, with disastrous effects.
- Greg Egan has written a short story called "Mitochondrial Eve".
- The anime/manga series K.R.I.E.G made several references to mitochondria and the existence of the Mitochondrial Eve theory, among many other theories of evolution and human creation.
- Arthur C. Clarke's novel The Light of Other Days describes a sequence where mitochondrial DNA is visually traced back to a Mitochondrial Eve.