Deep learning has shown remarkable potential for industrial applications, particularly in predictive maintenance and condition monitoring. A key challenge in this domain is prognostics, specifically predicting the Remaining Useful Life (RUL) of assets - a continuous value prediction problem. However, two critical challenges limit the effective deployment of deep learning models for RUL prediction in real-world industrial settings. First, the high variability of operating conditions and system configurations (such as different units of a fleet) leads to significant distribution shifts between training and deployment, resulting in substantial degradation of model performance. Second, in safety-critical systems, preventive maintenance practices prevent assets from reaching highly degraded states, resulting in severely imbalanced datasets that predominantly reflect early degradation states. While these challenges are common to both classification and regression tasks, they are more pronounced in regression tasks such as RUL prediction, as regression models are more sensitive to variations in input data and feature scaling, making generalization under domain shifts and data imbalance particularly challenging. Although domain adaptation methods have shown promise in mitigating distribution shifts, they have been primarily developed for classification tasks, with relatively limited research addressing the distinct characteristics of regression tasks. This dissertation addresses these real-world industrial challenges and proposes a comprehensive framework that effectively handles domain shifts and data imbalance in deep regression models. The thesis makes four main contributions. Firstly, we develop a phase-aware distribution alignment method that leverages expert knowledge to individually align overrepresented and underrepresented operational phases in the data. By aligning the marginal distributions of each operational phase separately across domains, this method improves RUL prediction accuracy and generalization across different operating conditions. Secondly, we introduce regression-specific adaptation methods based on closed-form solutions and uncertainty estimation. This contribution consists of two distinct methods. We propose aligning the inverse Gram matrices to preserve feature relationships and scales during the alignment, aiming to align the features from the regressor's perspective. Additionally, we incorporate uncertainty quantification to guide the adaptation process, providing confidence measures alongside predictions. This serves two purposes: to enrich the embedding space of regression models (which in computer vision tasks tends to be lower-rank than in classification) and to provide uncertainty estimates, not just point estimates, which is important for real-world deployment. Thirdly, we propose an in-context learning approach to address the challenge of imbalanced data distributions, particularly in learning from minority regions.