Abstract: The talk consists of two parts. In the first one, we describe the classical results on the existence of strong and weak solutions of the stochastic differential equation $dX_t=A(X_t)dt+B(X_t)dW_t$. In the second part, we concentrate our attention to the singular equations of the types $dX_t=-\operatorname{Sgn}X_t dt+dW_t$, $dX_t=\operatorname{Sgn}X_tdW_t$, $dX_t=\operatorname{I}(X_t>0)dW_t$, and $dX_t=\lambda dt+\operatorname{I}(X_t>0)dW_t$, with $\lambda<0$ and $\lambda>0$.