In the collection "Results of science and technology" . Series "Theor . likely. Mat. stat. Theory. Cybernet. ", Volume 23, M. : Ed. VINITI, 1985, C. 367. Abstract: The main results on the theory of Markov branching processes and branching processes with transformations depending on the age of particles, obtained from 1968 to 1983. Along with the traditional sections (integral and local limit theorems, stationary measures), the review contains sections devoted to statistics of branching processes. The list of references covers mainly works referenced in RZ Math. Bible . 497.