One significant cause of perioperative morbidity and mortality is intraoperative hemodynamic instability (IHI), which includes episodes of hypotension, hypertension, and arrhythmias. Current monitoring systems mainly alert clinicians when thresholds are violated, relying heavily on clinician alertness; therefore, they are reactive in nature and do not have sufficient sensitivity to detect the range of complex, multidimensional physiological trajectories that occur before IHI. This article will present a systematic review of the emerging multimodal deep learning (MDL) approaches to predicting IHI intraoperatively by using different sources of data to evaluate how heterogeneous continuous physiological waveforms (e.g., arterial blood pressure, ECG, SpO2, EEG), electronic health records (EHRs), anesthesia information management systems (AIMS), and imaging modalities can be fused and analyzed through early, late, or hybrid fusion architectures. We will examine neural networks, including convolutional neural networks (CNNs), long short-term memory (LSTM) networks, and transformer-based models, to determine their effectiveness for capturing both spatial and temporal signal characteristics relevant to the prediction of hemodynamics. Studies of apparent groundbreaking importance such as Hypotension Prediction Index (HPI) studies and VitalDB-based studies have shown that MDL models yield area under the receiver operating characteristic curve (AUROC) values between 0.91 and 0.95, along with clinically relevant lead times (5-15 minutes) before hemodynamic deterioration; resulting in significant improvements over standard statistical and univariate machine-learning baselines. Clinical studies to evaluate the efficacy of the MDL approach for clinician decision support have shown that the use of MDL-based decision support will reduce time-weighted average intraoperative hypotension by up to 50% relative to control groups in randomized controlled trials. Additionally, this review provides an overview of significant barriers (i.e., data heterogeneity, model generalizability, model bias, regulatory compliance, and ethical use) that must be overcome for successful implementation of an AI system in high-stakes operating rooms. Future directions for MDL systems include implementation of federated learning frameworks, the development of personalized adaptive predictive systems, and the utilization of explainable AI (XAI) to promote clinician confidence and enhance the equitable and safe use of MDL systems in diverse perioperative care environments.