Most experts agree that overfishing really started to happen in the 1950's and '60's. This is due in large part to the advance in technologies that allowed fishermen to locate larger schools of fish, to ranger farther from shore, as well as stronger machines to lift larger catches.
The depletion of these top predator species can cause a shift in entire oceans ecosystems where commercially valuable fish are replaced by smaller, plankton-feeding fish. This century may even see bumper crops of jellyfish replacing the fish consumed by humans.