Classification of smooth weak Fano threefolds of Picard number two

Smooth Fano threefolds have been classified through the works of Fano, Iskovskikh, Shokurov, Mori and Mukai. Threefolds whose anti-canonical class is nef and big, but not ample, are called weak Fano (or almost Fano). The aim of this talk is to briefly review the classification of smooth Fano threefolds and to report the recent results on the classification of smooth weak Fano threefolds of Picard number two.