I will discuss a series of our results related to semi-local dynamics near homoclinic tangencies. Special attention will be paid to bifurcations in first return maps. These maps will be presented their "normal forms", i.e., as polynomial maps which are approximations of rescaled first maps. We call these maps "homoclinic maps" since they arise from homoclinic orbits. Such maps are represented by the Henon map, the generalized Henon maps, some two-dimensional endomorphisms, three-dimensional Henon maps etc. Some questions of dynamics of these maps will be discussed. In particular, rather new results on existence of strange attractors (of Lorenz type) in 3D Henon maps will be presented.