By now, everyone knows that alaia is a term used to describe one type of surfboard ridden by Hawaiians in the old days. Thus, the new trend of riding alaias is a revival rather than an innovation. Here is a link to a great brief history of surfing in Hawaii.
Here are a couple of good excerpts from this history of surfing describing surfing in Hawaii before and just after Europeans showed up:
Before contact with Cook's crew, Hawai'i was ruled by a code of kapu(taboos) which regulated almost everything: where to eat; how to grow food; how to predict weather; how to build a canoe; how to build a surfboard; how to predict when the surf would be good, or convince the Gods to make it good. Hawaiian society was distinctly stratified into royal and common classes, and these taboos extended into the surf zone. There were reefs and beaches where the ali'i (chiefs) surfed and reefs and beaches where the commoners surfed. Commoners generally rode waves on paipo (prone) and alaia (stand up) boards as long as 12 feet, while the ali'i rode waves on olo boards that were as long as 24 feet.
[Description of surfing from a member of Captain Cook's crew] But a diversion the most common is upon the Water, where there is a very great Sea, and surf breaking on the Shore. The Men sometimes 20 or 30 go without the Swell of the Surf, & lay themselves flat upon an oval piece of plan about their Size and breadth, they keep their legs close on top of it, & their Arms are us'd to guide the plank, thye wait the time of the greatest Swell that sets on Shore, together push forward with their Arms to keep on its top, it sends them in with a most astonishing Velocity, the great art is to guide the plan so as always to keep it in a proper direction on the top of the Swell, as it alters its direct. If the Swell drives him close to the rocks before he is overtaken by its break, he is much prais'd. On first seeing this very dangerous diversion I did not conceive it possible but that some of them must be dashed to mummy against the sharp rocks, but jus before they reach the shore, if they are very near, they quit their plank, & dive under till the Surf is broke, when the piece of plank is sent many yards by the force of the Surf from the beach. The greatest number are generally overtaken by the break of the swell, the force of which they avoid, diving and swimming under the water out of its impulse. By such like excercises, these men may be said to be almost amphibious. The Women could swim off to the Ship, continue half a day in the Water, afterwards return. The above diversion is only intended as an amusement, not a tryal of skill, & in a gentle swell that sets on must I conceive be very pleasant, at least they seem to feel a great pleasure in the motion which this Exercise gives.