A product of graphs is a binary operation defined on the class of graphs. Much study has been done on the adjacency matrix and the Laplacian matrix of graphs. Here, we study the graphs realizing the product of matrices associated with graphs. We also deal with some matrix and combinatorial techniques to characterize graphs satisfying equations involving matrices related to graphs. In this survey article, the results pertaining to the realization of a product of graphs , the realization of modulo 2 product of graphs , some matrix equations of graphs , realization of A(G)A(GkP) , and an algorithm to check whether a given graph G has a companion  are discussed. A few new results and the scope for further exploration are also given.