The discovery of the first X-ray binary, Scorpius X-1, by Giacconi et al. (1962), marked the birth of X-ray astronomy. Following that discovery, many additional X-ray sources where found with the first generation of X-ray rockets and observatories (e.g., UHURU and Einstein). The short-timescale variations in their X-ray luminosity and the detection of the optical counterparts, established the binary nature of many of these X-ray sources. In such systems (the so-called X-ray binaries) a regular star is transferring material on to a neutron star (NS) or a black hole (BH). Half a century later and after several generations of X-ray instruments, many new phenomena have been discovered and studied. This led to new insights in fundamental fields like the behaviour of ultra-dense matter or in the theory of general relativity in extreme gravitational fields, among others.In the last decades, a new generation of X-ray telescopes with revolutionary capabilities, such as RXTE, XMM-Newton, Chandra or Swift have opened up previously inaccessible regions of study, improving our understanding of accreting compact objects. Their improvement in spatial resolution and sensitivity have made it possible to obtain high quality data at very low luminosities. This thesis focusses on the study of the family of subluminous of X-ray binaries, shedding new light on the properties at low accretion regimes and challenging current evolution and accretion models.