This thesis presents an overview of X-ray spectroscopy and applications to a particular class of astrophysical objects-accretion-powered X-ray sources. I use data obtained with the Advanced Satellite for Cosmology and Astrophysics (ASCA) to derived physical parameters of the high mass X-ray binary system Vela X-1 and the Circinus, a type 2 Seyfert galaxy, from detailed analyses of the X-ray spectra. I will also discuss some preliminary results from the high resolution observation of an archetypal Seyfert 2 galaxy Mkn 3 with the High Energy Transmission Grating Spectrometer onboard the Chandra X-ray observatory. I will demonstrate the power of X-ray spectroscopy, and show how it can be used to infer global properties of circumnuclear regions around compact objects.