Warren Abstract Machine (WAM) has become a generally accepted standard Prolog implementation technique. Garbage collection is an important aspect in the implementation of any Prolog system. We first present a synopsis of the WAM and then show marking and compaction algorithms that take advantage of WAM's unique use of the data areas. Marking and compaction are performed on both the heap and the trail. The marking and compaction algorithms use pointer reversal techniques, which obviate the need for extra stack space. However, two bits for every pointer on the heap are reserved for the garbage collection algorithm. The algorithm can work on segments of the heap, which may lead to a significant reduction of the total garbage collection time. The time of the algorithms are linear in the size of the areas.