The chapter introduces two stochastic processes that model the dispersal of cells or organisms in biological systems. The first process, called the position jump or kangaroo process, involves alternating pauses and fixed jumps, where the duration of pauses follows a waiting time distribution and the direction and distance of jumps are governed by an integral operator. Under certain assumptions, this process is described by a diffusion equation. The second process, the velocity jump process, consists of sequences of "runs" separated by reorientations, leading to a damped wave equation known as the telegrapher’s equation. The authors derive explicit expressions for mean squared displacement and other observable quantities, and discuss generalizations such as incorporating resting times. The chapter also reviews available data on cell and organism movement and explains how this data can be analyzed within the proposed framework.The chapter introduces two stochastic processes that model the dispersal of cells or organisms in biological systems. The first process, called the position jump or kangaroo process, involves alternating pauses and fixed jumps, where the duration of pauses follows a waiting time distribution and the direction and distance of jumps are governed by an integral operator. Under certain assumptions, this process is described by a diffusion equation. The second process, the velocity jump process, consists of sequences of "runs" separated by reorientations, leading to a damped wave equation known as the telegrapher’s equation. The authors derive explicit expressions for mean squared displacement and other observable quantities, and discuss generalizations such as incorporating resting times. The chapter also reviews available data on cell and organism movement and explains how this data can be analyzed within the proposed framework.