The document discusses the classification of fishes throughout history. It describes early classifications by Muller, Berg, and Romer, which divided fishes into 6, 7, and 4 classes respectively. The current and most widely accepted classification is Nelson's from 1994, which uses a cladistic approach and evolutionary relationships to arrange fishes into subclasses under the subphylum Vertebrata. Nelson's classification places fishes in the grade Pisces and divides them into classes like Placodermi and Osteichthyes.