Data mining is used for mining data from databases and finding out meaningful patterns from the database. Discovering Association Rules is a core topic of data mining. One of the challenges in developing association rules mining algorithms is the extremely large number of rules generated which makes the algorithms inefficient and makes it difficult for the end users to comprehend the generated rules. This paper aims at giving an overview to some of the previous researches done in this topic, evaluating the current status of the field, and envisioning possible future trends in this area. The theories behind association rules are presented at the beginning. Comparison of different algorithms is provided as part of the evaluation.