What are the limitations of using robust standard errors?

Robust standard errors primarily address heteroskedasticity. They do not correct for other violations of OLS assumptions like omitted variable bias, multicollinearity, or endogeneity. In very small samples, robust standard errors can still be unreliable. Furthermore, they don't solve the problem of inefficient coefficient estimates; OLS is still the Best Linear Unbiased Estimator (BLUE) under homoskedasticity.