Continuous-time time series demand models capable of reasoning over sparse, asynchronous, and multi-resolution observations while respecting the underlying dynamical structure. Modern continuous-time architectures address this challenge by parameterizing differential operators whose trajectories evolve through learned dynamics, enabling flexible interpolation, robust handling of irregular sampling, and principled uncertainty quantification through stochastic formulations. Frequency-domain and multi-scale representations further complement these models by decomposing signals across temporal resolutions, revealing regimes governed by heterogeneous dynamics. Graph-based continuous-time frameworks extend these ideas to systems with relational structure, allowing interactions among entities to evolve under time-varying dependencies. Transfer learning and online adaptation provide mechanisms for reusing learned dynamics across domains and updating models in streaming environments where distributional drift is inevitable. Neural ODEs, SDEs, and their hybrid variants unify these perspectives by casting forecasting as inference in continuous dynamical systems. Together, these techniques form a coherent foundation for learning, adapting, and generalizing in complex real-world scenarios where time flows continuously rather than discretely.