Ever since humans have fished the oceans we have considered the ocean's resources as infinite as the ocean seems to be. For quite some time, this was the case for the most part. Even the largest fishing fleets couldn't seem to make much of a dent in the stocks of any fish, shellfish, etc. Once industrialization began however, the story changed. The technological advancements of industrialization and the accompanying population boom generated both the demand and capability to drastically increase fishing efforts.
The early stages of overfishing are generally only measured by the gradual decrease in the average size of fish. As more and more are taken the average age that a fish lives to gets lower, meaning less time to grow and develop. If this continues for too long the number of reproductive age individuals will be so low that they can not efficiently find each other. This results in a "Population Collapse", as most mathematical estimations of population growth break down due to the inability of the remaining individuals to even reproduce. The population is not extinct at this point, but it often takes years of active rehabilitation before it returns to healthy levels.
This has happened multiple times within the last 50 years, and the unfortunate trend is to ignore the problem until it actually happens. The North Atlantic Cod fishery collapsed in 1992, several deep sea fish stocks, and even the Oyster fisheries near New York have all experienced collapse with some never recovering. Pressure for fishery regulation reform is always met with intense opposition from fishermen and corporations who would likely not be able to make a living under safe quotas, and refuse to accept the risk of collapse.
Recent activism has started to pay off in terms of smart conservation efforts. Since 2010 the Japanese government had been allowing more than 10,000 whales be taken per year for "Scientific Research". Recently a U.N. court ruled that Japan's "Scientific" whaling practices were illegal and ordered the Japanese Government to immediately halt all such operations. Unfortunately a lot of the world's fishing practices are unsustainable and still unregulated. Fishing that happens in international waters, such as tuna fishing, is one of the biggest concerns. If we don't move to further regulate the harvesting of marine resources we may soon not have anything to harvest at all.