This thesis consists of studies on the topic of relativistic stellar pulsations. i) A new formalism for the numerical study of g-modes in neutron stars is developed. This formalism avoids pitfalls associated with previous formalisms when applied to the study of these low-frequency modes. The formalism involves a new choice of perturbation variables, the introduction of an "instantaneous gravity" approximation to the field outside the star, and an energy principle for determining gravitational radiation damping times. The formalism is used to study g-modes that arise because of chemical inhomogeneities in neutron star crusts. g-mode frequencies associated with chemical inhomogeneities are found to be much higher than those associated with finite temperature. ii) The relativistic Cowling approximation, introduced by McDermott, Van Horn, and Scholl (1983) and analogous to the Newtonian Cowling approximation, is refined to make it more accurate in the regime of highly relativistic stars. The approximation is used to prove a host of useful theorems regarding the non-radial modes of relativistic stars. iii) Realistic neutron stars have a solid crust, and this will seriously affect their g-modes. The first steps toward developing a theory of non-radial relativistic pulsations in stars with a solid crust is reported on here: the calculation of the shear strain and stress during a pulsation, the introduction of the shear stress into the Einstein field equations as a source and to the equations of motion as a force, and the development of a Lagrangian and variational principle for studying non-radial relativistic pulsations in stars with a solid crust. iv) Solar five-minute oscillations are a weak source of gravitational radiation. The inner part of the solar system is actually in the transition zone of the solar oscillation gravitational field, and future space-based beam detectors might be able to measure the solar "transition-zone radiation." The transition-zone gravitational field is explored for four relativistic gravity theories: a spin-zero theory (Nordstøm's theory), a spin-one theory (analogous to electromagnetism), a spin-two theory (general relativity), and a mixed spin-zero/spin-one theory (Jordan-Brans-Dicke theory). From the transition-zone gravitational field, it is possible to determine experimentally the spin content of relativistic gravity.