  In this paper, we are concerned with convergence rate of Euler-Maruyama
scheme for stochastic differential equations with rough coefficients. The key
contributions lie in (i), by means of regularity of non-degenerate Kolmogrov
equation, we investigate convergence rate of Euler-Maruyama scheme for a class
of stochastic differential equations, which allow the drifts to be
Dini-continuous and unbounded; (ii) by the aid of regularization properties of
degenerate Kolmogrov equation, we discuss convergence rate of Euler-Maruyama
scheme for a range of degenerate stochastic differential equations, where the
drift is locally H\"older-Dini continuous of order $\frac{2}{3}$ with respect
to the first component, and is merely Dini-continuous concerning the second
component.
