Low‐pressure gas discharge plasmas are known to be strongly affected by the presence of small dust particles. This issue plays a role in the investigations of dust particle‐forming plasmas, where the dust‐induced instabilities may affect the properties of synthesized dust particles. Also, gas discharges with large amounts of microparticles are used in microgravity experiments, where strongly coupled subsystems of charged microparticles represent particle‐resolved models of liquids and solids. In this field, deep understanding of dust–plasma interactions is required to construct the discharge configurations which would be able to model the desired generic condensed matter physics as well as, in the interpretation of experiments, to distinguish the plasma phenomena from the generic condensed matter physics phenomena. In this review, we address only physical aspects of dust–plasma interactions, that is, we always imply constant chemical composition of the plasma as well as constant size of the dust particles. We also restrict the review to two discharge types: dc discharge and capacitively coupled rf discharge. We describe the experimental methods used in the investigations of dust–plasma interactions and show the approaches to numerical modelling of the gas discharge plasmas with large amounts of dust. Starting from the basic physical principles governing the dust–plasma interactions, we discuss the state‐of‐the‐art understanding of such complicated, discharge‐type‐specific phenomena as dust‐induced stratification and transverse instability in a dc discharge or void formation and heartbeat instability in an rf discharge.