This review discusses the recent advancements in understanding the physics of accretion flows in X-ray binaries, particularly black hole and neutron star binaries. It highlights how X-ray and radio data from these systems can be integrated with theoretical models to provide a coherent picture of the accretion process in strong gravitational fields. The review covers the behavior of both long-term X-ray light curves, X-ray spectra, rapid X-ray variability, and radio jet activity, which are consistent with a model where an outer accretion disc is truncated at low luminosities, replaced by a hot inner flow that also launches jets. The transition from the disc to the inner flow leads to softer spectra, higher frequencies, and faster jets. The collapse of the hot flow at the last stable orbit triggers a significant decrease in radio flux and explains the hard-soft spectral transition in black holes. Neutron stars exhibit similar behavior but with additional surface contributions, providing evidence for event horizons in black holes. The review also addresses observational data that conflict with this model but shows that they can be reconciled with the truncated disc model. Alternative models for the accretion flow, which do not involve a truncated disc, are discussed, but they generally converge on a similar geometry with a transition between a standard disc and an inner, jet-dominated region. The review emphasizes the importance of understanding accretion in strong gravity for various astrophysical phenomena, including the growth of galaxies and the reionization of the early universe. It also delves into the stability and time-dependent behavior of accretion discs, the hydrogen ionization instability, and the radiation pressure instability. The inner accretion flow, including the spectral states in Cyg X-1, is explored, and the role of optically thin flows and their stability is discussed. The review concludes by outlining a plausible model for the different spectral states observed in X-ray binaries, integrating the hot inner flow and truncated disc mechanisms.This review discusses the recent advancements in understanding the physics of accretion flows in X-ray binaries, particularly black hole and neutron star binaries. It highlights how X-ray and radio data from these systems can be integrated with theoretical models to provide a coherent picture of the accretion process in strong gravitational fields. The review covers the behavior of both long-term X-ray light curves, X-ray spectra, rapid X-ray variability, and radio jet activity, which are consistent with a model where an outer accretion disc is truncated at low luminosities, replaced by a hot inner flow that also launches jets. The transition from the disc to the inner flow leads to softer spectra, higher frequencies, and faster jets. The collapse of the hot flow at the last stable orbit triggers a significant decrease in radio flux and explains the hard-soft spectral transition in black holes. Neutron stars exhibit similar behavior but with additional surface contributions, providing evidence for event horizons in black holes. The review also addresses observational data that conflict with this model but shows that they can be reconciled with the truncated disc model. Alternative models for the accretion flow, which do not involve a truncated disc, are discussed, but they generally converge on a similar geometry with a transition between a standard disc and an inner, jet-dominated region. The review emphasizes the importance of understanding accretion in strong gravity for various astrophysical phenomena, including the growth of galaxies and the reionization of the early universe. It also delves into the stability and time-dependent behavior of accretion discs, the hydrogen ionization instability, and the radiation pressure instability. The inner accretion flow, including the spectral states in Cyg X-1, is explored, and the role of optically thin flows and their stability is discussed. The review concludes by outlining a plausible model for the different spectral states observed in X-ray binaries, integrating the hot inner flow and truncated disc mechanisms.