Objective: The paper focuses on development of robust and accurate processing solutions for continuous and cuff-less blood pressure (BP) monitoring. In this regard, a robust deep learning-based framework is proposed for computation of low latency, continuous, and calibration-free upper and lower bounds on the systolic and diastolic BP. Method: Referred to as the BP-Net, the proposed framework is a novel convolutional architecture that provides longer effective memory while achieving superior performance due to incorporation of casual dialated convolutions and residual connections. To utilize the real potential of deep learning in extraction of intrinsic features (deep features) and enhance the long-term robustness, the BP-Net uses raw Electrocardiograph (ECG) and Photoplethysmograph (PPG) signals without extraction of any form of hand-crafted features as it is common in existing solutions. Results: By capitalizing on the fact that datasets used in recent literature are not unified and properly defined, a benchmark dataset is constructed from the MIMIC-I and MIMIC-III databases obtained from PhysioNet. The proposed BP-Net is evaluated based on this benchmark dataset demonstrating promising performance and shows superior generalizable capacity. Conclusion: The proposed BP-Net architecture is more accurate than canonical recurrent networks and enhances the long-term robustness of the BP estimation task. Significance: The proposed BP-Net architecture addresses key drawbacks of existing BP estimation solutions, i.e., relying heavily on extraction of hand-crafted features, such as pulse arrival time (PAT), and; Lack of robustness. Finally, the constructed BP-Net dataset provides a unified base for evaluation and comparison of deep learning-based BP estimation algorithms.