In 1979 Reid discovered the 95 families of K3 surfaces in three dimensional weighted projective spaces. After
this, Fletcher, who was a Ph.D. student of Ried, discovered the 95 families of weighted Fano threefold hypersurfaces in his Ph.D. dissertation in 1988. These are quasi-smooth hypersurfaces of degrees d with only terminal singularities in weighted projective spaces P(1, a1, a2, a3, a4),where d = a1+a2+a3+a4.  All Reid’s 95 families of K3 surfaces arises as anticanonical divisors in Fletcher’s 95 families of Fano threefolds.  These Fano threefold hypersurfaces carry many fascinating properties. In my talk, I explain how to verify that  all the quasi-smooth Fano threefold hypersurfaces in the 95 familes are birationally rigid, which confirms the conjecture of Corti, Pukhlikov and  Reid. Since the entire proof is very long and adopts various methods, I will focus on one or two interesting families out of the 95 families.