The integral equation adjoint to the linear transport equation for neutrons is formulated and prescriptions given for its solution by Monte Carlo methods. The process of tracking is the same as for the usual (i.e., forward) Monte Carlo and may be applied to complex geometry. On the other hand, the scattering process is determined by a kernel which is the transpose of the one used in the forward equation. With the help of suitably defined “adjoint cross sections” this transposed kernel may be written as a superposition of density functions for different reaction types in different nuclides. It is then possible to sample nuclide and reaction sequentially as in the familiar Monte Carlo for the forward process. Most emphasis is put upon the solution of the analytical and numerical problems which arise in calculating and sampling the probability distributions which determine these scattering processes. Detailed treatment is given for generating and using the requisite data for elastic scattering, for discrete level and continuum inelastic neutron scattering: and for (n, 2n) reactions.