We describe here efforts to create and study magnetized electron–positron pair plasmas, the existence of which in astrophysical environments is well-established. Laboratory incarnations of such systems are becoming ever more possible due to novel approaches and techniques in plasma, beam and laser physics. Traditional magnetized plasmas studied to date, both in nature and in the laboratory, exhibit a host of different wave types, many of which are generically unstable and evolve into turbulence or violent instabilities. This complexity and the instability of these waves stem to a large degree from the difference in mass between the positively and the negatively charged species: the ions and the electrons. The mass symmetry of pair plasmas, on the other hand, results in unique behaviour, a topic that has been intensively studied theoretically and numerically for decades, but experimental studies are still in the early stages of development. A levitated dipole device is now under construction to study magnetized low-energy, short-Debye-length electron–positron plasmas; this experiment, as well as a stellarator device that is in the planning stage, will be fuelled by a reactor-based positron source and make use of state-of-the-art positron cooling and storage techniques. Relativistic pair plasmas with very different parameters will be created using pair production resulting from intense laser–matter interactions and will be confined in a high-field mirror configuration. We highlight the differences between and similarities among these approaches, and discuss the unique physics insights that can be gained by these studies.