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Accretion onto compact objects is one of the fundamental mechanisms for powering high energy emission in quasars, active galactic nuclei, and X-ray binaries. In this talk, I will present our study of relativistic accretion flow around various compact objects and discuss its astrophysical significance. We investigate relativistic accretion flows in the strong gravity regime around compact objects by incorporating the effective potential. The infalling rotating matter may encounter a centrifugal barrier, and depending on the shock conditions, a post-shock corona (PSC) of hot, dense electrons can form. PSC reprocesses the soft disk photons to high energy radiations via inverse Comptonization. We show that shock-induced accretion flows around Kerr-Taub-NUT BHs are thermodynamically favored and yield significantly higher luminosity than shock-free solutions. BHs are not the only possible accreting compact objects, exotic compact objects like wormholes (WHs) remain theoretically viable. Therefore, we investigate the relativistic accretion flow around Kerr-like WH and show that the accretion solutions around WH can explain the observed luminosity of Cygnus X-3 in its hypersoft state. In this framework, we further examine the impact of dark matter (DM) halos on accretion dynamics, considering that the BH is surrounded by a Hernquist, Navarro-Frenk-White (NFW), Einasto, or DM spike profile. DM shifts the critical points inward and enhances disk luminosity, which offers a potential probe of DM distribution near BHs. Finally, within a steady-state GRMHD framework, we model magnetized accretion around Kerr BHs motivated by Event Horizon Telescope observations of Sagittarius A*. Our solutions reproduce magnetic field strengths within ±10% of the EHT-constrained values, that provides a consistent theoretical description of magnetized accretion flows.