Since the early days of the controlled nuclear fusion program, plasma physics in general, and magnetically confined plasmas in particular, have been a source of Hamiltonian problems. In the spirit of the workshop that aims to bring together the plasma physics and mathematics communities, in this talk we present an overview of past and recent developments of plasma physics problems that have led to novel and challenging mathematical problems in Hamiltonian dynamical systems. Among the problems discussed are: nontwist systems, mean-field coupled Hamiltonian systems, non-autonomous symplectic maps, and gyro-averaged symplectic-maps. Some recent developments on relativistic dynamics of high-energy (runaway) electrons in fusion plasmas will also be discussed.