How many steps from state 0 to state 1 by a random walk? It is a key step in the research for the random walk in random environment by Kesten at al(1975)and can be traced back to Harris(1952)for the nearest random walk.By decompose the trajectory of the random walk,the steps can be counted in terms of a Galton-Watson branching processes.However,when the random walk is non-nearest the situation is essentially complicated.In this talk,I will review some progress on this topics by our group for the random walk with bounded jumps,where different multi-type branching structure within the random walk have been revealed.Some results on the random walk in random environment have been obtained based on the branching structure as a basic tool.And other applications such as explicit expression of the stationary distribution and criteria of the recurrence and transience,have been addressed as well.(The series work were jointly with Huaming Wang,Lin Zhang and Ke Zhou.)