Underwater wireless optical communication (UWOC) has attracted increasing interest in various underwater activities because of its order-of-magnitude higher bandwidth compared to acoustic and radio-frequency technologies. Testbeds and pre-aligned UWOC links were constructed for physical layer evaluation, which verified that UWOC systems can operate at tens of gigabits per second or close to a hundred meters of distance. This holds promise for realizing a globally connected Internet of Underwater Things (IoUT). However, due to the fundamental complexity of the ocean water environment, there are considerable practical challenges in establishing reliable UWOC links. Thus, in addition to providing an exhaustive overview of recent advances in UWOC, this paper addresses various underwater challenges and offers insights into the solutions for these challenges. In particular, oceanic turbulence, which induces scintillation and misalignment in underwater links, is one key factor in degrading UWOC performance. Novel solutions are proposed to ease the requirements on pointing, acquisition, and tracking (PAT) for establishing robustness in UWOC links. The solutions include light-scattering-based non-line-of-sight (NLOS) communication modality as well as PAT-relieving scintillating-fiber-based photoreceiver and large-photovoltaic cells as the optical signal detectors. Naturally, the dual-function photovoltaic-photodetector device readily offers a means of energy harvesting for powering up future IoUT sensors.