| Fano varieties (with mild singularities) appear naturally in the minimal model program as building blocks for the large class of the outcome varieties (the so called Mori fiber spaces). On this way classification of Fano 3-folds is important for study of birational geometry of 3-dimensional algebraic varieties. Smooth Fano 3-folds have been classified in the papers of Iskovskikh, Mori and Mukai. However, very little is known in the singular case. In my talk I will speak about one particular class of singular Fano 3-fods, namely, those which have canonical Gorenstein singularities. I will consider some partial results on classification of these varieties, further developments in this direction and applications to the moduli and arithmetic problems for surfaces. |