We propose to investigate in this thesis a class of astrophysical objects termed as compact objects. Black holes and neutron stars falls into this classification. BHs cannot be directly observed (“being black”) but its presence can be confirmed through the huge amount of energy they liberate through a process called accretion. Similarly, accreting X-ray neutron stars have also been observed. They also exist as radio pulsars and can be directly observed through radio telescopes. Thus, there is a need to model these flows in order to map their environment as well as guess their presence. This thesis is focussed on studying these accretion flows as well as anaysing their spectrum for a broad range of parameter space, in order to have a knowledge of the underlying physics present in these systems. Accretion flows around BHs predict inner disc temperatures which are optimal enough to give rise to pair production and annihilation. It is interesting to note, that an annihilation line has been observed near mec 2 , which confirms that pairs indeed play an important role in accretion disc physics as well as in shaping the observable spectum. Extracting a proper spectrum of an accretion flow using two-temperature theory has also been done. Since electrons are the ones which radiate, knowledge of electron temperature is necessary to compute a spectrum. We addressed a long outstanding problem of degeneracy in two-temperature solutions. Here, we proposed a novel methodology to remove it, which is the main highlight of my thesis work.