Abstract: Objective: Urban activity flows record the movement processes and spatial interactions of individuals and groups within the built environment, providing a dynamic basis for understanding transport operations, urban functional organization, spatial supply-demand relationships, and population differences. With advances in multisource spatiotemporal observation and geocomputational methods, research has moved beyond aggregate origin-destination statistics toward the coordinated representation of movement processes, spatial structures, and their underlying mechanisms. A systematic review of representative methodological advances helps clarify the progression from spatiotemporal representation and structural analysis to dynamic prediction. Methods: The review is organized around three interconnected dimensions: spatiotemporal modeling, analysis, and prediction. Path-flow and vector-field approaches are examined as representative discrete and continuous forms of activity-flow representation. Adaptive flow clustering and geographically constrained spatiotemporal tensor models are used to summarize developments in heterogeneous pattern identification and traffic anomaly diagnosis. Turn-level traffic forecasting on heterogeneous road networks and activity-flow generation and distribution prediction incorporating socioeconomic and demographic attributes are further discussed. Attention is given to the research objects, methodological characteristics, analytical capabilities, limitations, and interrelationships of these approaches. Results: Path flows represent individual trips as ordered spatiotemporal sequences composed of road network semantic units and preserve route choice, turn movements, temporal processes, traffic states, and individual congestion exposure. Vector-field modeling converts discrete trajectories or path flows into continuous or quasi-continuous spatial fields, enabling the characterization of movement direction, intensity, directional complexity, and congestion potential across scales. These methods extend activity-flow representation from endpoint connections to traceable movement processes and macroscopic directional structures. Adaptive flow clustering integrates spatial statistical tests, information measures, and density-based structures to identify flow clusters with different shapes, densities, and spatial scales while reducing dependence on empirically specified parameters. Spatiotemporal tensor models organize traffic states by road segment, time of day, and date, and combine low-rank and sparse decomposition with constraints on network topology and temporal continuity to distinguish recurrent patterns from event-related anomalies. Activity-flow analysis therefore progresses from aggregate flow statistics toward multiscale structural identification and geographically constrained anomaly diagnosis. In prediction, heterogeneous road-network models represent road segments and intersection turns as different node types and explicitly encode their directional relationships, supporting coordinated prediction across network elements. Deep gravity models enhance conventional spatial-interaction models while retaining origin attributes, destination attributes, and spatial impedance. The incorporation of socioeconomic and demographic attributes enables comparisons of built-environment associations among population groups, while explainable machine-learning methods quantify global and local variable contributions. Conclusions: Urban activity-flow research is undergoing three major transitions: from endpoint statistics to the coordinated representation of paths, processes, and fields; from single-scale pattern extraction to multiscale structural analysis and event-process diagnosis; and from aggregate predictive accuracy to the joint consideration of network heterogeneity, population differences, and model interpretability. Spatiotemporal modeling provides the basis for identifying activity-flow structures and dynamic changes, while analytical findings support the formulation and interpretation of predictive models. Future research should develop integrated space-air-ground observation systems, clarify cross-scale relationships among individual movement, route processes, network propagation, and urban spatial patterns, and integrate transport mechanisms and behavioral constraints with deep learning. Further attention should be given to prediction stability under sparse observations, changes in urban structure, and unexpected disruptions, as well as crosscity transferability, privacy protection, sample representativeness, and external validation of population differences. Activity-flow-based monitoring and evaluation systems can provide dynamic information support for the evaluation of territorial spatial planning implementation, urban health assessment, and refined urban governance.