A century ago, Sir Ronald Ross and Karl Pearson proposed to apply random walks for modelling the migration of organisms. This stochastic approach was later refined by using the Langevin equation, which describes the Brownian motion of a tracer particle in a fluid. However, a tracer is passively driven by molecular collisions while the movement of biological agents is self-propelled leading to the concept of active particles. In parallel, advanced stochastic models yielding anomalous diffusion beyond Brownian motion were put forward to describe organismic movements. In this book chapter, we first introduce the three research areas underlying the above scenario, which are movement ecology, active matter and anomalous diffusion. Then we show that they need to be combined in terms of generalised Langevin dynamics for understanding the movements of organisms. For this purpose, we construct generalised Langevin equations from statistical experimental data analysis of bumblebee flights, migrating cells and foraging sea turtles, which reveal active and anomalous properties. Inspired by movement ecology, we then put forward a particular generalised Langevin equation for modelling organismic movement, which blends key ingredients of the three fields of research referred to above. We discuss experimental applications of this equation and outline its theoretical foundation.