A survey of some new results on empirical Edgeworth expansions and the $M$ out of $N$ bootstrap accuracy for trimmed means and studentized trimmed means will be presented. We discuss the second order correctness of the $M$ out of $N$ ($N$ being the real data sample size, $M$ denotes the size of the bootstrap resample) bootstrap, provided the trimmed mean is properly defined and a local smoothness condition on the underlying distribution is satisfied. We also assume a relation between $M$ and $N$, as $\min (M,N)$ gets large. In practical applications, the $M$ out of $N$ bootstrap requires extensive Monte Carlo simulations. To reduce the computation time one can take $M$ of smaller order than $N$, i.e. $M/N$ approaches zero as $\min ( M,N )$ gets large, and apply the bootstrap in conjunction with extrapolation.