Estimating Remaining Useful Life (RUL) and predicting bearing faults based on data-driven models have become central components of modern Prognostics and Health Management (PHM) systems. Although deep learning models have demonstrated strong performance under controlled and stationary operating conditions, their reliability in real-world industrial and marine environments is limited. In practice, operating conditions, sensor properties, and degradation mechanisms evolve continuously over time, leading to non-stationary and shifting data distributions that violate the assumptions of conventional static learning approaches. To address these challenges, two research areas have gained increasing attention: Domain Adaptation (DA), which aims to mitigate distribution discrepancies across operating conditions or machines, and Continual Learning (CL), which enables models to learn sequentially while mitigating catastrophic forgetting. However, existing studies often examine these paradigms in isolation, limiting their effectiveness in long-term deployments, where domain shifts and temporal evolution coexist. This paper presents a comprehensive and systematic review of data-driven bearing fault prognosis and RUL prediction under evolving data distributions, adopting the framework of Domain-Adaptive Continual Learning (DACL). By jointly examining the DA and CL methods, this review analyzes how these approaches have been individually and implicitly combined to cope with nonstationarity, knowledge retention, and limited label availability in practical PHM scenarios. We categorised existing methods, highlighted their underlying assumptions and limitations, and critically assessed their applicability to long-term, real-world monitoring systems. Furthermore, key open challenges, including scalability, robustness under sequential domain shifts, uncertainty handling, and plasticity–stability trade-offs, are identified, and research directions are outlined based on the identified limitations and practical deployment requirements of the proposed method. This review aims to establish a structured and critical reference framework for understanding the role of domain-adaptive CL in data-driven prognostics, clarifying current research trends, limitations, and open challenges in evolving data distributions.