The subject of this review article is the motion of a point scalar charge, a point electric charge and a point mass in a given background spacetime. The review begins with a description of the general theory of bitensors (tensorial functions of two points in spacetime). Synge’s world function, its derivatives, the parallel propagator and the van Vleck determinant are introduced. A convenient coordinate system is constructed (retarded coordinates) with the help of a Fermi-Walker transported tetrad along the world line of the point particle. The next chapter considers distributions in curved spacetime, while in the next parts the retarded, advanced, singular and radiative Green’s functions for scalar, vectorial and tensorial wave equations are introduced. Due to this complete description of the necessary mathematical tools it is easy to follow the final construction of the retarded, singular and radiative fields associated with a point scalar charge, a point electric charge and a point mass.