There exist evidences that magnetic field in the vicinity of astrophysical black holes plays an important role. In particular it is required for explanation of such phenomenon as jet formation. Study of such problems in all their complexity requires 3D numerical simulations of the magnetohydrodynamics in a strong gravitational field. Quite often when dealing with such a complicated problem it is instructive to consider first its simplifications, which can be treated either analytically, or by integrating ordinary differential equations. Motion of a charged particle in a weakly magnetized black hole is an important example. We consider a non-rotating black hole in the weak magnetic field which is homogeneous at infinity. In the talk I discuss the following problems: How does such a magnetic field affect charged particle motion in the equatorial plane? How does it change the radius of the innermost stable circular orbits (ISCO) and period of rotation? I shall demonstrate that the magnetic field increases the efficiency of the energy extraction from the black hole and that magnetized black holes can be used as "particle accelerators". Finally, I shall discuss out of equatorial plane motion and demonstrate that it is chaotic. Possible applications of these results to astrophysics are briefly discussed.