Chronic stress is a time-dependent condition characterized by sustained dysregulation across neural, autonomic, and endocrine systems, with important consequences for both health and socioeconomic outcomes. Unlike acute stress, which is typically characterized by short-lived physiological activation, chronic stress reflects an accumulated allostatic load and a longer-term recalibration of stress response systems. Recent advances in physiological sensing and artificial intelligence (AI) have supported the development of computational approaches for chronic stress detection using electroencephalography (EEG), heart rate variability (HRV), photoplethysmography (PPG), electrodermal activity (EDA), and wearable multimodal platforms. This narrative review examines current AI-based studies through three main inferential paradigms: resting baseline dysregulation, longitudinal physiological monitoring, and reactivity-based inference. Across modalities, classical machine learning (ML) methods, particularly support vector machines (SVMs) and tree-based ensembles, remain the most commonly used approaches, largely because available datasets are small and most pipelines still depend on engineered features. Deep learning (DL) methods are beginning to emerge, but their use remains constrained by the lack of large, standardized, longitudinal datasets specifically designed for chronic stress research. Major challenges include ambiguity in stress labeling, limited longitudinal validation, circadian confounding, inter-individual variability, and small cohort sizes. Future progress will depend on standardized datasets, biologically grounded multimodal integration, hybrid baseline-reactivity modeling, adaptive personalization, and more interpretable AI systems. Greater emphasis is also needed on clinical relevance and generalizability if AI-based chronic stress monitoring is to move beyond experimental settings.