Protists, an umbrella term first coined by Ernst Haeckel in 1866, are a vast collection of (primarily unicellular) eukaryotes that are "neither animals nor plants". This basic definition by exclusion has been exercised for centuries, even though recent advances have led to more rigorous taxonomic assignment of various protist groups. Pioneering comparative phylogenetic approaches have been applied to these organisms to reconstruct the deep branches of the eukaryotic tree, revealing essential clues about early eukaryotic evolution. Protists, including amoebae, flagellates, ciliates, and algae, are also vital constituents of global ecosystems, where they appear at the base of food chains, control the relative abundance of other microbes, and participate in global biogeochemical recycling. Due to their typically small size and lack of nervous systems, protists are often associated with the unfortunate label 'primitive'. Yet they exhibit remarkable behavioural sophistication and are able to feed, predate, navigate and interact with their surroundings. Unlike macroscopic animals, many protists reside in a non-intuitive physical regime where viscous forces dominate over inertia, and where they use diverse propulsion and navigation strategies. Interdisciplinary research into these cell-scale phenomena, characterised by a complex interplay of physical forces and mechanical constraints, has significantly advanced the emerging fields of active matter, microhydrodynamics, and non-equilibrium statistical physics. This primer discusses the biophysics of protist behaviour, with a focus on locomotion and feeding. I will highlight the most extensively studied principles and describe some more esoteric behaviours that have not yet been systematically explored.