The work contains a brief survey of research related to stochastic and quasistochastic methods of computation carried out in recent years by the author and his colleagues. The areas of research include, in particular, substantiation of multiplicative generators of pseudorandom numbers, Monte Carlo methods for solving nonlinear equations, complexity estimation, stochastic stability and parallelism of stochastic and quasistochastic algorithms. This area of research is of utmost current interest in view of the rapid development of multiprocessor computing machinery.