This dissertation focuses on compact binaries, located in globular clusters and the Galactic disk. Using optical and X-ray observations, various properties and parameters of binaries are determined. In particular, we study the binary population of Galactic globular clusters. By searching for optical counterparts to X-ray sources located in globular clusters, we can identify and classify X-ray emitting binaries. Comparison of the types and numbers of binaries between different globular clusters allows one to set constraints on the formation mechanisms of the separate binary classes. We furthermore investigate three binaries containing millisecond pulsars. For the first, we obtain constraints on its membership with a globular cluster and determine the physical properties of the binary companion and the mass of the pulsar. For the second system, the rotational properties of the pulsar should have a significant impact on the binary companion, but these effects are not seen. Through accurate astrometry, we show that the pulsar properties are likely in error, solving a curious problem of this system. For the last system, we expected to find a hot white dwarf, but a cool one was found instead. We investigate scenarios to explain the observations. In the last part, we study two low-mass X-ray binaries and find indirect evidence which supports the notion that these two systems have ultra-compact orbits. A similar third system, which was an active X-ray source for a decade, is not seen in recent X-ray observations, constraining the cooling of the neutron star. Furthermore, its optical counterpart is also not detected, confirming the notion that the system is also ultra-compact
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