In response to increasing demands for reliability and uptime, organizations are progressively monitoring more of their mission-critical assets through various sensing and data collection devices. The accumulated data enables several emerging technologies, particularly data-driven approaches such as machine learning, which are becoming more viable in industrial contexts. These technologies have the potential to enhance the effectiveness and efficiency of asset management and maintenance. A key framework for realizing this potential is prognostics and health management, an engineering approach that deals with the identification and prognostication of system degradation. A major aspect of prognostics and health management is remaining useful life prediction, which develops models to forecast the remaining operational time of systems. Accurate prediction of future system state provides useful insight that aids maintenance planning. This thesis addresses challenges and aspects of data-driven remaining useful life prediction with a focus on deep learning-based approaches. The research proposes solutions to key challenges in remaining useful life prediction, including limited access to complete run-to-failure trajectories, data sharing constraints, and decentralized training requirements. Additionally, this thesis investigates remaining useful life predictions for discrete power electronics, components used in safety-critical high-power applications such as automotive systems -- an area that remains understudied within prognostics and health management. The findings demonstrate that remaining useful life prediction is a viable technology in these domains, with models benefiting from self-supervised pretraining and decentralized training through federated learning. Furthermore, the research establishes that discrete power electronics can be effectively monitored using data-driven remaining useful life prediction methods.