For a positive integer n, the partition function p(n) of n is defined by the number of distinct ways of representing n as a sum of positive integers. Starting with the congruence properties of partition numbers discovered by Ramanujan over a century ago, research on the congruence properties of partition numbers has progressed actively. Moreover, the relationship between the generating function of the partition function and a modular form has significantly advanced the study of these congruence properties. Despite this progress, many aspects of the congruence properties of partition numbers remain unknown. In this talk, I will introduce various congruence properties of partition function and open questions in this area. Also, I will briefly introduce the relationship between a modular form and the partition function.