With energy outputs >~10^51 erg in 0.1-1000 seconds, Gamma-ray Bursts (GRBs) are the most powerful events yet observed in the Universe. As such they are potential probes of the very early Universe, back to the era of re-ionisation and the first stars, but at the same time they have been observed to span a wide range in luminosity and redshift from the relatively local Universe (z~0.0085) out to z~6.29. GRBs divide into two classes based primarily on their duration as measured by T90 (the time taken to observe 90% of the total burst fluence). Long bursts (L-GRBs) have T90>~2 seconds, and shorts (S-GRBs) T90<~2 seconds. Though much has been learned regarding long duration GRBs since the first afterglow discovery in 1997 (including their likely association with massive core collapse supernovae), much remains unknown regarding short duration GRBs. In this work, after a brief historical introduction and review, we present analyses of the angular cross-correlation on the sky of short GRBs from the BATSE catalogue with galaxies in the local Universe sampled from the PSCz Redshift Survey and the Third Reference Catalogue of Bright Galaxies (RC3). In particular we show that 20%+/-8% (1 sigma) of all BATSE short duration bursts (localised to 10 degrees or better) show correlation with galaxy samples (morphological T-type<=4) within ~112 Mpc. Our statistics thus provide evidence that a substantial fraction of BATSE short GRBs show a tendency to be associated with large scale structure on the sky traced by a variety of galaxy types. Short GRBs are believed to be produced in the final merger of compact object (neutron star-neutron star or neutron star-black hole) binaries, though other possible progenitors are known to exist. The short initial spike of a giant flare from a Soft Gamma Repeater (SGR) such as the December 27th 2004 event from SGR1806-20 would have been detectable by BATSE as a short GRB if it occurred in a galaxy within ~30-50 Mpc (assuming a distance to SGR1806-20 of 15 kpc). Using the observed luminosities and rates of Galactic SGR giant flares, as well as theoretical predictions for the rate of binary mergers, we investigate the ability of plausible Luminosity Functions (LF), singly and in combination, to reproduce our observed correlations and a cosmological S-GRB population. We find the correlations are best explained by a separate population of lower luminosity S-GRBs, with properties consistent with them being due to giant flares from extra-galactic SGRs. Overall predicted number counts are a good fit to the observed BATSE number counts, and furthermore, the wider redshift distribution is consistent with the early Swift S-GRB redshift distribution. The three closest GRBs which have been observed to date were all long duration bursts, and we have therefore also searched for cross-correlation signals between the BATSE long GRBs and local galaxies. The three nearby bursts shared several similar properties such as being under-luminous, spectrally soft and of low variability. We have therefore also investigated a subset of L-GRBs with light curve properties similar to these known nearby bursts. The whole sample is found to exhibit a correlation level consistent with zero (1 sigma upper limit=10%, equivalent to 144 bursts) out to a radius of ~155 Mpc, but a spectrally soft, low observed fluence and low variability subset shows a correlation level of 28%+/-16% (=50+/-28 bursts) within 155 Mpc. These results are consistent with low-luminosity, low-variability bursts being a separate sub-class of L-GRBs which may be much more prevalent in the local Universe than their high-luminosity, cosmologically distant counterparts. To investigate this further, we once again examined plausible luminosity functions for single and dual high and low luminosity populations, based on observed intrinsic rates from the literature. The local population was once again found only to be produced to a sufficient level (while maintaining consistency with the observed overall number counts) by a separate low luminosity population with intrinsic rates several hundred times greater than their cosmological counterparts. Constraining the models via the Swift overall redshift distribution instead of threshold-adjusted BATSE number counts showed that the dual LF models were able to produce excellent fits to the entire redshift distribution while adequately reproducing a local population. Finally, suggestions are made as to the direction future work may follow in order to build on these initial investigations, as well as to how observations with future missions and detectors such as Fermi (formerly GLAST), Advanced LIGO and LOFAR may shed further light on nearby GRBs.

This thesis concerns with the study of X-ray binaries which are gravitationally bound systems consisting of a compact object (either a neutron star or a black hole) and usually a non degenerate companion star, both rotating around the common centre of mass. The compact star shines brightly in the X-ray regime. Emission from these systems are powered by accretion which is the most radioactively efficient mechanism known in the universe by the release of gravitational potential energy when matter from the companion star falls on the compact object. Accretion onto high magnetic field neutron stars are special as the magnetic field plays a crucial role in governing the dynamics of gas flow and the flow of the matter close to the compact object. The radiation emitted from these systems are anisotropic and for a distant observer, the intensity is modulated at the spin period of the neutron star, hence these objects are called accretion powered pulsars. The angular pattern of the emitted radiation is also highly anisotropic and depends on the mass accreted and hence the luminosity. The beaming pattern commonly known as the pulse profiles exhibit a wide variety in the pulse shape and pulse fraction and vary with energy as well as intensity. They also exhibit cyclotron absorption features in their energy spectrum which are a direct probe to the magnetic field geometry of these systems. This thesis is dedicated to the study of the magnetic field and emission geometry of accretion powered pulsars through the pulse phase resolved studies of the cyclotron absorption features which are a direct probe of the magnetized plasma. In order to study these features in detail broadband continuum modeling of the energy spectrum is done, taking care of all other factors which may smear the pulse phase dependence. Another prerequisite for detailed continuum modeling is accounting for the low absorption dips in the pulse profiles of many these sources. The dips are presumably formed by phase locked accretion stream causing partial covering absorption when the stream is along our line of sight towards the emission region. Studying the pulse phase dependence of this partial covering absorber also provides us with important clues on the local environment of the neutron star and the structure of the accretion stream. All of these studies are performed with data from the broadband and most sensitive instruments onboard the Japanese satellite Suzuki. Lastly we provide estimates of the polarization expected to be detected from these sources by a Thomson scattering polarimeter being developed to observe the polarization of X-rays in the energy range of 5--30 keV. Along with the X-ray pulsars, we also make an estimate of the likelihood of detection of X-ray polarization from black hole X-ray binaries in different spectral states. This is a particularly interesting topic as it will play a crucial role in providing additional handles on the magnetic field geometry in accretion powered pulsars as well as constrain the fundamental parameters of a black hole like its spin.