In the year 1988 Guo [1] introduced the integral modification of Meyer Konig and Zeller operators and studied the rate of convergence for functions of bounded variation. Gupta [2] gave the sharp estimates for these operators. This paper is an extensive survey on the Meyer-K¨onig and Zeller operators. It includes most of the modifications they have undergone through the years. We compute rate of convergence of the defined operators by means of modulus of continuity.