Seventeen years of hard X-ray observations with the instruments of the INTEGRAL observatory, with a focus on the Milky Way and in particular on the Galactic Centre region, have provided a unique database for exploration of the Galactic population of low-mass X-ray binaries (LMXBs). Our understanding of the diverse energetic phenomena associated with accretion of matter onto neutron stars and black holes has greatly improved. We review the large variety of INTEGRAL based results related to LMXBs. In particular, we discuss the spatial distribution of LMXBs over the Galaxy and their X-ray luminosity function as well as various physical phenomena associated with Atoll and Z sources, bursters, symbiotic X-ray binaries, ultracompact X-ray binaries and persistent black hole LMXBs. We also present an up-to-date catalogue of confirmed LMXBs detected by INTEGRAL, which comprises 166 objects. Last but not least, the long-term monitoring of the Galactic Centre with INTEGRAL has shed light on the activity of Sgr A* in the recent past, confirming previous indications that our supermassive black hole experienced a major accretion episode just ~100 years ago. This exciting topic is covered in this review too.
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