  In order to classify and understand the spacetime structure, investigation of
the geodesic motion of massive and massless particles is a key tool. So the
geodesic equation is a central equation of gravitating systems and the subject
of geodesics in the black hole dictionary attracted much attention. In this
paper, we give a full description of geodesic motions in three-dimensional
spacetime. We investigate the geodesics near charged BTZ black holes and then
generalize our prescriptions to the case of massive gravity. We show that
electric charge is a critical parameter for categorizing the geodesic motions
of both lightlike and timelike particles. In addition, we classify the type of
geodesics based on the particle properties and geometry of spacetime.
