| Summary: | The interaction of strong magnetic fields of compact objects with the surrounding plasma leads to novel and puzzling astrophysical phenomena. In this dissertation, we examine some of the properties of strongly magnetized plasmas as outlined in the following. A fully relativistic treatment of Bernstein waves in a uniform, magnetized, relativistic electron-positron pair plasma has remained too formidable a task owing to the very complex nature of the problem. We perform contour integration of the dielectric response function and numerically compute the dispersion curves. If coupled to electromagnetic modes, these waves may be important for generating radiation in pulsar magnetospheres. The soft gamma-ray repeaters, classified as magnetars, unleash large amounts of magnetically stored energy in a spectacular event called the giant flare. What causes these flares to develop is an open question. We examine two trigger mechanisms, one internal and the other external to the neutron star. In the internal mechanism, we propose that the strongly wound up poloidal magnetic field develops tangential discontinuities and dissipates its torsional energy in heating the crust. Alternatively, we argue that the shearing motion of the external magnetic field footpoints causes the materialization of a Sweet-Parker current layer in the magnetosphere. The thinning of this macroscopic layer powers the giant flare. The extreme environments of compact objects are conducive to the creation of exotic particles, that may not be discovered in laboratories. The light pseudoscalar particle, dubbed the axion, borne out of the Peccei-Quinn solution to the strong CP problem in QCD is one such particle which remains elusive. We present a novel way of constraining its properties by examining the level of linear polarization in the radiation emerging from magnetic white dwarfs. On sub-meV mass scales, our study provides the strongest constraints on axion properties obtained astrophysically. The cooling theory of neutron stars is corroborated by comparison with observations of thermally emitting isolated neutron stars. An important ingredient for such an analysis is the age of the object, which typically is highly uncertain. We conduct a population synthesis study of the nearby isolated thermal emitters and obtain their ages statistically.
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