| Several aspects of observations of neutron stars and compact extragalactic radio sources are considered, with particular regard to their use in constraining certain astrophysical phenomena.; A theoretical treatment of the pulse arrival time analysis of millisecond pulsars is made; we consider how a detailed timing analysis can be used to quantitatively probe noise processes affecting the pulsar period and the propagation of the radiation. The intrinsic noise may be used to study the neutron star interior, while propagation effects due to gravitational perturbations of the neutron star and interstellar refraction of the emitted radio waves provide probes of the pulsar environment and the intervening plasma. In addition, important constraints on the background of cosmological gravitational radiation can be derived from timing such pulsars.; We consider the thermal X-rays emitted from a warm {dollar}(10sp5{lcub}rm K{rcub}{dollar} {dollar} |