Memristive devices change their resistance state upon appropriate voltage stimuli. The resistance change can have a different physical origin, e.g. configuration of ionic defects, phase changes or the orientation of the magnetization. These devices offer at least two stable (non‐volatile) resistance states and could be thus used as memory devices. In recent times, however, further applications moved into the focus of world‐wide research activities. Different computation‐in‐memory (CIM) concepts were demonstrated, such as stateful logic operations, vector‐matrix multiplication or solving of linear equation systems. These concepts rely on the non‐volatile storage of multi‐level/analog resistance states. In addition, other properties of memristive devices were exploited. The intrinsic switching variability could be exploited for learning algorithm using stochastic synaptic updates, creating true random number generators, or for security applications as in physical unclonable functions (PUF). Moreover, volatile switching properties have been used to build resonator circuits for reservoir computing applications. In this lecture, an overview over different CIM applications of memristive devices will be given. The focus will lie on explaining the dynamic properties of memristive devices which enable these applications.