We report on recent progress in our theoretical understanding of X-ray binaries, which has largely been driven by new observations, and illustrate the interplay between theory and observations considering as examples intermediate-mass X-ray binaries, irradiation-driven evolution, ultraluminous X-ray sources and neutron stars with low-velocity kicks.

Non-linear oscillations in the accretion disk are favored as an explanation of high-frequency QPOs observed in the light curves of low-mass X-ray binaries containing neutron stars, black holes, or white dwarfs.

We have monitored the quasi-persistent neutron-star X-ray transient MXB 1659-29 in quiescence using Chandra. The purpose of our observations was to monitor the quiescent behavior of the source after its last prolonged outburst episode and to study the cooling curve of the neutron star in this system. We discuss the results obtained and how they constrain the properties of the neutron star in MXB 1659-29.

The optical counterpart of the binary millisecond X-ray pulsar SAX J 1808.4-3658 during quiescence was detected at V = 21.5 mag, inconsistent with intrinsic emission from the fain companion star. We propose that the optical emission from this system during quiescence is due to the irradiation of the companion star and a remnant accretion disk by the rotational energy released by the fast spinning neutron star, switched on, as magneto-dipole rotator (radio pulsar). In this scenario the companion behaves as a bolometer, reprocessing in optical part of the power emitted by the pulsar. The reprocessed fraction depends only on known binary parameters. Thus the blackbody temperature of the companion can be predicted and compared with the observations. Our computations indicate that the observed optical magnitudes are fully consistent with this hypothesis. In this case the observed optical luminosity may be the first evidence that a radio pulsar is active in this system in quiescence.

Globular clusters (GCs) harbour a large number of close binaries which are hard to identify optically due to high stellar densities. Observing these GCs in X-rays, in which the compact binaries are bright, diminishes the over-crowding problem. Using the new generation of X-ray observatories, it is possible to identify populations of neutron star low mass X-ray binaries, cataclysmic variables and millisecond pulsars as well as other types of binaries. We present the spectra of a variety of binaries that we have identified in four GCs observed by XMM-Newton. We show that through population studies we can begin to understand the formation of individual classes of binaries in GCs and hence start to unfold the complex evolutionary paths of these systems.