We review our studies on spin-dependent phenomena in various colloidal nanocrystals (quantum dots, dot-in-rod, and nanoplatelets). Several magneto-optical techniques are used in high magnetic fields: magnetic-field-induced polarization of neutral and charged excitons, spin-flip Raman scattering, and pump-probe Faraday rotation. We focus on spin properties and spin dynamics of neutral and charged excitons in order to identify them and measure g-factors and spin relaxation times. Pump-probe time-resolved Faraday rotation experiments with additional prepump allow us to measure coherent spin dynamics of carriers in CdS NCs at room temperature, and to study interplay between the negative and positive photocharging processes. We discuss the role of the dangling bond spins for recombination of the dark excitons and for formation of the dangling bond magnetic polaron.