The purpose of the talk is to investigate the Lp(IRd) (1 < p < ∞) boundedness and the behavior L1(IRd) , d ≥ 2, of some singular integral operators with rough kernels, the commutators of rough singular integral operators, and some maximal singular integral operators with rough kernels, which are not within the scope of the standard Calder´on-Zygmund theory.