The purpose of this survey is to present Moran sets and Moran classes which generalize the classical selfsimilar sets from the following points: (i) The placements of the basic sets at each step of the constructions can be arbitrary; (ii) the contraction ratios may be different at each step; and (iii) the lower limit of the contraction ratios permits zero. In this discussion we will present geometrical properties and results of dimensions of these sets and classes, and discuss conformai Moran sets and random Moran sets as well.