Hyperelliptic and trigonal Fano threefolds
  We classify Fano 3-folds with canonical Gorenstein singularities whose anticanonical linear system has no base points but does not give an embedding, and we classify anticanonically embedded Fano 3-folds with canonical Gorenstein singularities which are not intersections of quadrics. We also study the rationality questions for most of these varieties. 
Ivan Cheltsov, Constantin Shramov, Victor Przyjalkowski