In this paper,a survey is given for the investigation on the stability of numerical schemes of stochastic differential equations in the past years.As a related topic,the convergence of the schemes is involved.The paper introduces the achieved results by literatures for the classical Itô stochastic differential equations,stochastic functional differential equations of the neutral type,and the stochastic differential equations with Markov or Poisson jumps.The involved numerical schemes include the Euler-Maruyama scheme,the Backward Euler-Maruyama scheme,the θ scheme,and the split-step scheme,etc.The paper analyzes the academic thoughts in some classical literatures on the stability equivalence theorems and proposes some problems and challenges for further investigations on the numerical computations and simulations of stochastic differential equations at the end of the paper.