A review of the recent results concerning the new concepts and achievements in the area of semiconductor spintronics (or spin-electronics) is presented. Because spin-orbit interactions (SOI) couple electron spins to electric fields and allow electrical manipulation of electron spins and electrical detection of spin dynamics they form the fundamental mechanisms of new effects and the basis of different proposals for new spintronic devices. In addition to known channels of SOI in semiconductor materials and heterostructures, new terms of SOI, induced by interband interaction through the electrical polarization or atomic displacement like optical phonons are proposed and analyzed in the paper. These SOI 7mechanisms have the physical nature in the relativistic quantum mechanics with Lorentz boosts and this aspect is highlighted. Some particularities of the electronic states of semiconductor quantum wells (QW) related to the intrinsic Rashba SOI and Rashba like S vbOI induced by the electrical polarization (EP) are studied. Size quantization states are shown to transform into interface ones at some value of the in-plane QW wave vector under SOI effect. Tunneling characteristics of single barrier heterostructure are analyzed in the conditions of both types of SOIs and are established to be spin-dependent under SOI induced by the EP. Several aspects dealing with the new discovered intrinsic spin and angular momentum Hall effects (SHE and AMHE) are revealed. The SHE is investigated in a two dimensional electron system with the SOI of both intrinsic and EP induced types. New peculiarities of SHE and AMHE , induced by interband interaction of heavy and light holes are studied in p-doped semiconductors with band degeneracy in the framework of generalized Luttinger Hamiltonian. Spin-conductivity induced by the EP is shown to proportional to difference of the inverse values of the hole wave vectors.