The underwater path planning problem deals with finding an optimal or sub-optimal route between an origin point and a termination point in marine environments. The underwater environment is still considered as a great challenge for the path planning of autonomous underwater vehicles (AUVs) because of its hostile and dynamic nature. The major constraints for path planning are limited data transmission capability, power and sensing technology available for underwater operations. The sea environment is subjected to a large set of challenging factors classified as atmospheric, coastal and gravitational. Based on whether the impact of these factors can be approximated or not, the underwater environment can be characterized as predictable and unpredictable respectively. The classical path planning algorithms based on artificial intelligence assume that environmental conditions are known apriori to the path planner. But the current path planning algorithms involve continual interaction with the environment considering the environment as dynamic and its effect cannot be predicted. Path planning is necessary for many applications involving AUVs. These are based upon planning safety routes with minimum energy cost and computation overheads. This review is intended to summarize various path planning strategies for AUVs on the basis of characterization of underwater environments as predictable and unpredictable. The algorithms employed in path planning of single AUV and multiple AUVs are reviewed in the light of predictable and unpredictable environments.