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Low-Mass X-ray Binaries in Globular Clusters: Puzzles and Solutions

In dense stellar systems, dynamical interactions between objects lead to frequent formation of exotic stellar objects, unusual binaries, and systems of higher multiplicity. They are especially important for the formation of low mass X-ray binaries (LMXBs), which are not only formed 100 times more efficiently than in the field, but also have a puzzling dependence on metallicity. In this contribution we review how compact objects are formed and retained, the mechanisms of dynamical formation and the specifics of the evolution of mass-transferring binaries with neutron stars and black holes in globular clusters - those two kinds of compact objects have different favored paths to become luminous in X-ray. We describe how stellar evolution affects ostensibly purely dynamical formation, producing the observed metallicity dependence for LMXBs. We also discuss the next puzzle to be solved on our journey to understand the link between LMXBs and millisecond pulsars formation.