Identical twins start out as genetically identical: they have the same alleles. They both share the same sack in the womb They are always of the same sex, and are monozygotic or MZ twins (mono = one; zygote = fertilised egg). This contrasts with fraternal twins, who are formed by two separate eggs fertilised by two separate sperms, and who are not always the same sex (DZ = dizygotic). Both types of twin are carried in the same uterus at the same time, so their birth environment is the same.

Research shows that the frequency of monozygotic twinning is one in 240 births. Fraternal twins are twice as common. In vitro fertilization (IVF) techniques are more likely to create dizygotic twins. For IVF deliveries, there are nearly 21 pairs of twins for every 1,000.

Twin research 
Identical twins are natural clones. Because they start out with the same genes, they can be used to investigate how much heredity contributes to individual people. This is the nature vs nurture question.

Studies with twins have been quite interesting. If we make a list of characteristic traits, we find that they vary in how much they owe to heredity. For example:
Eye colour: entirely inherited.
Weight, height: partly inherited, partly environmental.
Which language you speak: entirely environmental.

The way the studies are done is like this. Take a group of identical twins and a group of fraternal twins, and a group of siblings from the population. Measure them for various traits. Do a statistical analysis (such as analysis of variance). This tells you to what extent the trait is inherited. You will find that all those traits which are partly inherited will be significantly more similar in identical twins.

Studies like this may be carried further, by comparing identical twins brought up together with identical twins brought up in different circumstances. That gives a handle on how much circumstances can alter the outcomes of genetically identical people.

Modern research has shown quite clearly that genetic inheritance does influence psychological aspects of life (how people behave), not just physical aspects.

History 

The person who first did twin studies was Francis Galton, Darwin's half-cousin, who was a founder of statistics. His method was to trace twins through their life-history, making many kinds of measurement. Unfortunately, though he knew about mono and dizygotic twins, he did not appreciate the real genetic difference. Twin studies of the modern kind did not appear until the 1920s.

Wilhelm Weinberg made the first estimate of the rate of twinning. Realizing that identical twins would have to be the same sex, while non-identical twins could be either same or opposite sex, Weinberg derived a formula for estimating the frequency of MZ and DZ twins from the ratio of same and opposite sex twins to the total of maternities. Weinberg also estimated that the heritability of twinning itself was close to zero. That means the capacity to have twins is not hereditary.

Not quite so identical 
Monozygotic twins are genetically nearly identical and they are always the same sex unless there has been a mutation during development. Monozygotic twins always have different phenotypes. Twins may express different sexual phenotypes, normally from an XXY Klinefelter's syndrome zygote splitting unevenly.

Although monozygotic twins are genetically almost identical, a 2012 study of 92 pairs of monozygotic twins found that monozygotic twins acquire hundreds of genetic differences early in fetal development. This is caused by mutations (or copy errors) taking place in the DNA of each twin after the splitting of the embryo. Another study in 2018 of 450 pairs of monozygotic twins showed that often (87%) the two twins varied in sexuality. the study also showed that if one twin married before 40, the other was also likely to marry before 40.

It is estimated that, on average, a set of monozygotic twins will have about 360 genetic differences that occurred early in fetal development.

Another cause of difference between monozygotic twins is epigenetic modification. These are caused by differing environmental influences throughout their lives, which affects which genes are switched on or off. A study of 80 pairs of monozygotic twins ranging in age from three to 74 showed that the youngest twins have relatively few epigenetic differences. The number of epigenetic differences increases with age. Fifty-year-old twins had over three times the epigenetic difference of three-year-old twins. Twins who had spent their lives apart (such as those adopted by two different sets of parents at birth) had the greatest difference. However, certain characteristics become more alike as twins age, such as IQ and personality. This phenomenon illustrates the influence of genetics in many aspects of human characteristics and behaviour.

Twins in animals 
Twinning is normal in many mammals, such as rats, cats, dogs. Identical twins are normal in a few species. The nine-banded armadillo, Dasypus novemcinctus, gives birth to identical quadruplets.

Offspring produced by non-sexual methods, such as parthenogenesis, are identical unless crossing over takes place in the production of eggs.

References 

Biological reproduction
Developmental biology
Classical genetics