 The class of protoalgebraic logics turned out to be the class of logics for which the theory of logical matrices works really well in the sense that many results of universal algebra have counterparts for the classes of reduced matrix models of these logics and many methods of universal algebra can be adapted to its study; consequently the algebraic study of protoalgebraic logics using their matrix semantics has been extensively and very fruitfully pursued. But, as we will see, some interesting logics are not protoalgebraic.