Spin related effects in electronic transport through quantum dots, coupled via tunneling barriers to two metallic leads, are discussed from the point of view of fundamental physics and possible applications in spin electronics. The effects follow either from long spin relaxation time in the dots or from spin dependent tunneling through the barriers when the external leads are ferromagnetic. In the former case large nonequilibrium spin fluctuations in the dot can be induced by flowing current. These fluctuations modify transport characteristics, particularly the shape of the Coulomb steps. In the latter case electric current depends on magnetic configuration of the system, and tunnel magnetoresistance effect due to magnetization rotation can occur. Transport properties in the weak coupling regime are described perturbatively in the first (sequential) and second (cotunneling) orders. In the strong coupling regime, on the other hand, the equation of motion for nonequilibrium Green functions is used to calculate electric current at low temperatures, where the Kondo peak in conductance is formed in the zero bias regime. In symmetrical systems the Kondo peak is split in the parallel magnetic configuration, whereas no splitting occurs for the antiparallel alignment. Theoretical results are discussed in view of available experimental data.