Low-Mass X-ray Binaries (LMXBs) are luminous (typically, 10^32 – 10^39 erg s^-1 in the X-ray band) X-ray objects among the binary systems. The LMXB consists of a compact object such as neutron star (NS) or stellar-mass black hole (BH) and a low-mass companion.  Matter from the companion star forms an “accretion disk” around the compact object, and then the accretion disk emits intense X-rays by the release of its gravitational potential energy.  I will present the latest results of the X-ray observations of the Galactic and extragalactic LMXBs, utilizing the Chandra, XMM-Newton, and the Suzaku satellites.  In my talk, the main topics of their X-ray properties are as follows: (1) the X-ray emission mechanism, including the redshifted Fe-K emission line, and (2) the luminosity function of the LMXBs.