Dynamic processes generating time series are a phenomenon occurring in many events and systems worth studying. This thesis explores how different algorithms can learn from time series in order to analyze and predict systems ranging from simple linear time series generating processes to more complex systems. In order to achieve this we develop a framework based on two core ideas: How to frame problems across different domains in a unifying state-space framework, and what kind of generalisable parametric and non-parametric model architectures can be applied to tackle these problems. We introduce a novel methodology combining models from computational physics as well as econometrics and epidemiology to show how multiple problems can be cast in a dynamical systems perspective and be studied by the inter-disciplinary models we introduce. We thus provide a generalisable framework for inference in multiple domains and furthermore show how the proposed parametric models are extendable using purely data-driven approaches.