  We summarize our investigations of several aspects of $\mathcal{N}=1$
supersymmetric Yang-Mills (SYM) theory. We present our final results for SU(3)
$\mathcal{N}=1$ SYM simulated with Wilson fermions. We also discuss the first
test of the simulations of the theory with overlap gluinos. Finally, we present
some recent progresses concerning the phase structure of the compactified
theory on $R^3\times S^1$.
