The geography of terminal Fano threefolds with Picard rank 1

Following papers by Y. Prokhorov, Y. Kawamata, M. Reid, K. Suzuki, I will tell the current picture of what is known about the geography of terminal Fano threefolds with Picard rank 1 with respect to the following biregular invariants: the Fano index, the degree, the minimal codimension of an embedding into a weighted projective space and dimensions of “anticanonical” linear systems.