In this paper, the discharge voltage is utilized as a critical indicator towards the probabilistic estimation of the Remaining Useful Life until the End-of-Discharge of the Lithium-Polymer batteries of unmanned aerial vehicles. Several discharge voltage histories obtained during actual flights constitute the in-house developed training dataset. Three data-driven prognostic methodologies are presented based on state-of-the-art as well as innovative mathematical models i.e. Gradient Boosted Trees, Bayesian Neural Networks and Non-Homogeneous Hidden Semi Markov Models. The training and testing process of all models is described in detail. Remaining Useful Life prognostics in unseen data are obtained from all three methodologies. Beyond the mean estimates, the uncertainty associated with the point predictions is quantified and upper/lower confidence bounds are also provided. The Remaining Useful Life prognostics during six random flights starting from fully charged batteries are presented, discussed and the pros and cons of each methodology are highlighted. Several special metrics are utilized to assess the performance of the prognostic algorithms and conclusions are drawn regarding their prognostic capabilities and potential.