Supernova remnants are beautiful astronomical objects that are also of high scientific interest, because they provide insights into supernova explosion mechanisms, and because they are the likely sources of Galactic cosmic rays. X-ray observations are an important means to study these objects.And in particular the advances made in X-ray imaging spectroscopy over the last two decades has greatly increased our knowledge about supernova remnants. It has made it possible to map the products of fresh nucleosynthesis, and resulted in the identification of regions near shock fronts that emit X-ray synchrotron radiation. In this text all the relevant aspects of X-ray emission from supernova remnants are reviewed and put into the context of supernova explosion properties and the physics and evolution of supernova remnants. The first half of this review has a more tutorial style and discusses the basics of supernova remnant physics and thermal and non-thermal X-ray emission. The second half offers a review of the recent advances.The topics addressed there are core collapse and thermonuclear supernova remnants, SN 1987A, mature supernova remnants, mixed-morphology remnants, including a discussion of the recent finding of overionization in some of them, and finally X-ray synchrotron radiation and its consequences for particle acceleration and magnetic fields.