A-site-ordered AA'BO quadruple perovskites (with twelve-fold coordinated A and square-planar coordinated A' sites) were discovered in 1967. Since then, there have been considerable research efforts to synthesize and characterize new members of such perovskites. These efforts have led to the discoveries of many interesting physical and chemical properties, such as inter-site charge transfer and disproportionation, giant dielectric constant, multiferroic properties, reentrant structural transitions and high catalytic activity. The first member of A-site columnar-ordered AA'A''BO quadruple perovskites (with ten-fold coordinated A, square-planar coordinated A' and tetrahedrally coordinated A'' sites), CaFeTiO, was discovered in 1995, and for 19 years it was the only representative of this family. In the last few years, AA'A''BO perovskites have experienced rapid growth. Herein, we present a brief overview of the recent developments in this field and highlight an under-investigated status and great potential of AA'A''BO, which can be prepared mainly at high pressure and high temperature. The presence of the A'' site gives an additional degree of freedom in designing such perovskites. The AA'A''BO perovskites are discussed in comparison with well-known AA'BO perovskites.