In this chapter we have summarised the problems of fast matrix multiplication algorithms. We gave a chronological overview of the main milestones in the field. Then we showed how the efficiency exponent of multiplication algorithms decreases over the years and discussed some theoretically obtained limits. Next, we presented a universal method for using matrix multiplication algorithms designed for square matrices for rectangular problems. We also presented a problem of speeding up matrix multiplication by choosing an order of parenthesis in the case of finding a multiple matrix multiplication.