Continuous-time modelling provides a mathematically principled framework for systems in which observations are irregular, event-driven, and governed by latent dynamics. In healthcare, it enables individualized inference from electronic health records by capturing physiological evolution between asynchronous clinical measurements. In financial forecasting, continuous-time stochastic processes model volatility, liquidity shocks, and trend formation at high-frequency scales. In Internet of Things and autonomous systems, they describe sensor interactions and control dynamics across heterogeneous, asynchronous networks. By representing evolution through differential operators, stochastic processes, and latent flow models, continuous-time approaches support smooth interpolation, uncertainty quantification, counterfactual reasoning, and robust extrapolation. Bridging theoretical machinery with domain-specific inference, continuous-time analysis offers a unified mathematical substrate for understanding and predicting the behaviour of complex real-world systems.