Type IIn supernovae (SNe) are characterized by narrow lines on a broad base in their optical spectrum. A wide diversity in their lightcurves, and in SNe that exhibit IIn features, has greatly complicated the task of identifying their progenitors. IIns have the highest X-ray luminosity of all SN classes, and are observable in X-rays decades after explosion.  Many of the lightcurves tend to fall off rather steeply at late times, although one interesting case displayed a rising light curve for several thousand days. These characteristics, along with their high luminosities at other wavelengths, imply initial expansion in a very dense medium in most cases. At later times the densities decrease faster than expected for expansion in a steady wind. Their X-ray spectra generally show distinct lines, suggesting that the emission is thermal in origin.  A recent exciting entry to the category of X-ray SN was the discovery by our group of a Type Ia-CSM, SN 2012ca, the first Type Ia SN of any kind to be detected in X-rays. Our best fit model for the X-ray emission from SN 2012ca suggests that it is expanding into a 2-component medium, with a density around 10$^8$ cm$^{-3}$ for the higher density component. Although the nature of these objects is unknown, we show that the X-ray properties of SN 2012ca are very similar to those of many Type IIn SNe.   We have compiled a database of lightcurves of most young SNe that have been detected in X-rays. We will show the X-ray lightcurves of IIns and the single Type Ia-CSM, and compare their lightcurves and spectra to those of other types of SNe. We will review the known properties of the X-ray emission from Type IIn, and explore the implications for the SN environment, progenitor mass-loss and the identity of the progenitors.