In underwater acoustic wireless sensor networks (UAWSNs), energy harvesting either enhances the lifetime of a network by increasing the battery power of sensor nodes or ensures battery-less operation of nodes. This, in effect, results in sustainable and reliable operation of the network deployed for various underwater applications. This work provides a survey of the energy harvesting techniques for UAWSNs. Our work is unique than the existing work on underwater energy harvesting in that it includes state-of-the art techniques designed in the last decade. It analyzes every harvesting scheme in terms of its main idea, merits, demerits and the extent of the harvested power (energy). The description of the merits results in selection of the suitable scheme for the suitable underwater applications. The demerits of the addressed schemes provide an insight to their future enhancement and improvement. Moreover, the harvested techniques are classified into various categories depending upon the involved energy harvesting mechanism and compared based on the maximum and minimum amount of harvested power, which helps in selection of the suitable category keeping in view the power budget of an underwater network before deployment. The challenges in energy harvesting and in UAWSNs are described to provide an insight to them and to address them for further enhancement in the harvested extent. Finally, research directions are specified for future investigation.