There is probably no better account of how such creatures became rare than The Unnatural History of the Sea by Callum Roberts. See the gallery on the book's web site for extraordinary historical images.
The elimination of giant fish in the world's fresh waters is probably even further advanced than it is in the seas [1, 2], with few initiatives such as Zeb Hogan's Megafishes Project struggling against the flow to save animals such as the giant catfish of the Mekong.
Hucho taimen, 'the river god's daughter', is the world's largest trout. It thrives, in Mongolia, by not being eaten.As Roberts and others have documented so well, shifting environmental baselines -- collective amnesia surrounding how things were more than a few decades ago -- are a nearly universal feature of human awareness. Go back hundreds or thousands of years and the abundance and size of fish in Europe seems beyond belief today. Roberts quotes Pliny the Elder, writing in the first century AD about sturgeon from the river Padus (the Po) as "sometimes reach[ing] almost half a ton (450kg) and [being] dragged from the water only by teams of oxen." 
Mesopotamian mythology tells of Oannes, an amphibious being who taught mankind wisdom. Oannes had the form of a fish but the head of a man under his fish’s head and the feet of a man under his fish’s tail. In the daytime he came up to the seashore of the Persian Gulf and instructed mankind in writing, the arts, and the sciences. 
Some scholars say one should think again before laughing at people who associated the divine with a river fish. Historically, many carp in the two rivers may well have been man-sized or bigger, and must have been an impressive sight in the murky waters. But the story turns bleak. In 2007 Iraqi mullahs put a fatwa on consumption of Tigris carp because the fish had grown fat on the many human bodies dumped into the rivers since liberation.
Just about the only image of hope and regeneration in Cormac McCarthy's The Road concerns freshwater fish:
Once there were brook trout in the streams in the mountains. You could see them standing in the amber current where the white edges of their fins wimpled softly in the flow. They smelled of moss in your hand. Polished and muscular and tortional. On their backs were vermiculate patterns that were maps of the world in its becoming. Maps and mazes. Of a thing which could not be put back. Not be made right again. In the deep glens where they lived all things were older than man and they hummed of mystery.Footnotes:
1. Can the human being and fish coexist peacefully? Yes, say Tim McClanahan and co-authors (Healing small-scale fisheries by facilitating complex socio-ecological systems). But the study does not focus on extraction of large animals.
2. See also, for example, Sunfish on this blog.
3. Continued heavy fishing and, in the medieval period, the rapid spread of mills diminished fisheries in European rivers so far that people were obliged to turn to the seas on a scale never seen before. The craft they developed surely played an important role in making Europe's age of expansion and conquest possible.
4. According to some accounts, Oannes was the emissary of Ea, god of the freshwater deep and of wisdom. Ea, also known as Ia (two syllables) is declined with the Semitic ending as Iahu and may have developed into the later form Yahweh. See here. In Hindu mythology Matsya, the first avatar of Vishnu, is a fish that dives into the ocean, rips open the stomach of rampaging demon and retrieves the Vedas.
Deep time holds even bigger fish than the deep waters of the Holocene. Consider, for example Dunkleosteus, a late Devonian placoderm, and Xiphactinus, a bony fish of the late Cretaceous which could swallow creatures up to 2m long whole.