Neutral heavier group 13 metals aluminum, gallium, and indium have been utilized as Lewis acid catalysts in various organic transformations ranging from classical organic reactions to polymerization reactions. The introduction of cationic charge can enhance the Lewis acidity of metal centers and allow cationic group 13 complexes to be excellent catalysts in Lewis acid catalysis, including most of the transformations achieved with neutral group 13 complexes. While cationic aluminum complexes have been investigated extensively in catalysis, there is a more recent push to explore the catalytic reactivities of cationic gallium and indium complexes. The field of cationic group 13 complexes has been expanding with discrete cationic complexes supported by purposely designed ligands. This review aims to provide an overview of what has been done to date and ideas of what can be possibly done from now in the growing field of cationic group 13 complexes as catalysts.