R-process
The r-process is a nucleosynthesis process occurring in core-collapse supernovae (see also supernova nucleosynthesis) responsible for the creation of approximately half of the neutron-rich atomic nuclei that are heavier than iron.  The process entails a succession of rapid  neutron captures on iron seed nuclei, hence the name r-process.  The other predominate mechanism for the production of heavy elements is the s-process, which is nucleosynthesis by means of slow neutron captures, primarily occurring in AGB stars, and together these two processes account for a majority of galactic chemical evolution of elements heavier than iron.

# History
The r-process was seen to be needed from the relative abundances of isotopes of heavy elements and from a newly published table of abundances by Hans Suess and Harold Urey in 1956. Among other things, this data showed abundance peaks for Germanium, Xenon, and Platinum. According to quantum mechanics and the nuclear shell model, radioactive nuclei that decay into isotopes of these elements have closed neutron shells near the neutron drip line.  This implies that some abundant nuclei must be created by rapid neutron capture, and it was only a matter of determining what other nuclei could be accounted for by such a process.  A table apportioning the heavy isotopes between s-process and r-process was published in a famous review paper in 1957, which proposed the theory of stellar nucleosynthesis and set the frame-work for contemporary nuclear astrophysics.

# Nuclear physics
Immediately after a core-collapse supernova, there is an extremely high neutron flux (on the order of 1022 neutrons per cm2 per second) and temperature, so that neutron captures occur much faster than beta-minus decays far from stability, meaning that the r-process "runs up" along the neutron drip line.  The only two hold-ups inhibiting this process of climbing the neutron drip line are a notable decreases in the neutron-capture cross section at nuclei with closed neutron shells, and the degree of nuclear stability in the heavy-isotope region, which terminates the r-process when such nuclei become readily unstable to spontaneous fission (currently believed to be in the neutron-rich region near A  = 270 (number of nucleons) in the chart of nuclides).  After the neutron flux decreases, these highly unstable radioactive nuclei quickly decay to form stable, neutron-rich nuclei.  So, while the s-process creates an abundance of stable nuclei with closed neutron shells, the r-process creates an abundance of nuclei about 10 Atomic mass units below the s-process peaks, as the r-process nuclei decay back towards stability on a constant A  line in the chart of nuclides.

# Astrophysical sites
The most widely believed candidate site for the r-process are core-collapse supernovae (spectral Type Ib, Ic and II), which provide the necessary physical conditions for the R-process.  However, the abundance of r-process nuclei requires that either only a small fraction of supernovae eject r-process nuclei to the interstellar medium, or that each supernova ejects only a very small amount of r-process material.  A recently proposed alternative solution is that neutron star mergers (a binary star system of two neutron stars that collide) may also play a role in the production of r-process nuclei, but this has yet to be observationally confirmed.