Blood pressure (BP) is a crucial indicator of cardiovascular health. Hypertension is a common life-threatening condition and a key factor of cardiovascular diseases (CVDs). Identifying abnormal BP fluctuations can allow for early detection and management of hypertension and related CVDs. Current clinical BP measurement methods are either invasive or obtrusive. Photoplethysmography (PPG)-based technologies have been identified as a promising means for continuous, non-invasive, and non-obtrusive BP monitoring. This thesis investigates whether data-driven approaches based on the PPG waveform could address the shortcomings of current BP monitoring technologies. This thesis first focuses on feature engineering approaches and analysis of the PPG pulse morphology (PWA). We expand the set of features by considering characteristic points derived from the PPG waveform, along with its first, second, and third derivatives. Our feature relevance analysis highlights the most important features for modeling BP and helps discuss their physiological consistency with cardiovascular parameters related to BP changes. We also investigate different machine learning algorithms for mapping the selected features to BP values. These models show good agreement with an invasive reference, as well as good ability to track rapid acute BP changes induced by anesthesia. The approach based on handcrafted features is then challenged with a feature learning model. This model uses a convolutional-based feature extractor to automatically identify relevant representations from an ensemble average PPG pulse and its derivatives, and estimates BP accordingly. It incorporates a single initial calibration measure through a Siamese architecture. When evaluated on a large dataset with a wide range of BP values, this model shows a high degree of correlation with the invasive reference and good trending ability. The process is less sensitive to signal quality and less dependent on the precise identification of PWA-based features. The improvement over a physiological model and the feature engineering model confirms the ability of the feature learning model to automatically capture relevant information in the PPG signal related to BP, beyond that present in handcrafted features. To mitigate the limitations of data-driven approaches in the number of available samples and model interpretability, we propose a new strategy to guide the learning process with some well-known physical principles related to BP regulation. It combines a two-element Windkessel model with a neural network architecture. The physical component cannot fully describe the underlying phenomenon relating PPG to BP, and the data-driven component helps to capture missing information. This hybrid model performs better than the purely physics-based model and can operate in a lower data regime than the purely feature learning approach. Overall, this thesis reveals various challenges related to continuous, non-invasive and non-obtrusive BP monitoring. Our observations mark the sensitivity of different data-driven approaches to available data, that is, the number of samples, signal quality, inter- and intra-subject variability of BP values. We also stress the importance of an initial calibration measure to minimize the impact of individual physiology on the PPG waveform. Our work opens up new directions for developing PPG-based BP monitoring technologies in ambulatory and clinical settings.