The most effective way to reduce the effect of vortex fluctuations in a superconductor, is to pin them down by introducing impurities. Columnar defects can be created by heavy ion irradiation, and is being actively investigated. On the other hand there are always some amount of point-like crystalline defects such as oxygen deficiencies in actual samples which can also trap a segment of the vortex line which comes along. In such systems, the combined effects of strong thermal fluctuation and a random potential due to defects, makes this important problem a very difficult subject. Our purpose here is to gain reliable knowledge on this issue through systematic large-scale numerical simulations. Displayed here is our phase diagram of the vortex system in the presence of point defects. This work was the first to theoretically derive all four of the phases indicated - including the vortex slush phase - from a single model. We are now also investigating the vortex system in the presence of columnar defects along similar lines.