Aging critical infrastructures and valuable machineries together with recent catastrophic incidents such as the collapse of Morandi bridge, or the Gulf of Mexico oil spill disaster, call for an urgent quest to design advanced and innovative prognostic solutions, and efficiently incorporate multi-sensor streaming data sources for industrial development. Prognostic health management (PHM) is among the most critical disciplines that employs the advancement of the great interdependency between signal processing and machine learning techniques to form a key enabling technology to cope with maintenance development tasks of complex industrial and safety-critical systems. Recent advancements in predictive analytics have empowered the PHM paradigm to move from the traditional condition-based monitoring solutions and preventive maintenance programs to predictive maintenance to provide an early warning of failure, in several domains ranging from manufacturing and industrial systems to transportation and aerospace. The focus of the PHM is centered on two core dimensions; the first is taking into account the behavior and the evolution over time of a fault once it occurs, while the second one aims at estimating/predicting the remaining useful life (RUL) during which a device can perform its intended function. The first dimension is the degradation that is usually determined by a degradation model derived from measurements of critical parameters of relevance to the system. Developing an accurate model for the degradation process is a primary objective in prognosis and health management. Extensive research has been conducted to develop new theories and methodologies for degradation modeling and to accurately capture the degradation dynamics of a system. However, a unified degradation framework has yet not been developed due to: (i) structural uncertainties in the state dynamics of the system and (ii) the complex nature of the degradation process that is often non-linear and difficult to model statistically. Thus even for a single system, there is no consensus on the best degradation model. In this regard, this thesis tries to bridge this gap by proposing a general model that able to model the true degradation path without having any prior knowledge of the true degradation model of the system. Modeling and analysis of degradation behavior lead us to RUL estimation, which is the second dimension of the PHM and the second part of the thesis. The RUL is the main pillar of preventive maintenance, which is the time a machine is expected to work before requiring repair or replacement. Effective and accurate RUL estimation can avoid catastrophic failures, maximize operational availability, and consequently reduce maintenance costs. The RUL estimation is, therefore, of paramount importance and has gained significant attention for its importance to improve systems health management in complex fields including automotive, nuclear, chemical, and aerospace industries to name but a few. A vast number of researches related to different approaches to the concept of remaining useful life have been proposed, and they can be divided into three broad categories: (i) Physics-based; (ii) Data-driven, and; (iii) Hybrid approaches (multiple-model). Each category has its own limitations and issues, such as, hardly adapt to different prognostic applications, in the first one, and accuracy degradation issues, in the second one, because of the deviation of the learned models from the real behavior of the system. In addition to hardly sustain good generalization. Our thesis belongs to the third category, as it is the most promising category, in particular, the new hybrid models, on basis of two different architectures of deep neural networks, which have great potentials to tackle complex prognostic issues associated with systems with complex and unknown degradation processes.