Lead halide perovskites (LHPs) in the form of nanometre-sized colloidal crystals, or nanocrystals (NCs), have attracted the attention of diverse materials scientists due to their unique optical versatility, high photoluminescence quantum yields and facile synthesis. LHP NCs have a 'soft' and predominantly ionic lattice, and their optical and electronic properties are highly tolerant to structural defects and surface states. Therefore, they cannot be approached with the same experimental mindset and theoretical framework as conventional semiconductor NCs. In this Review, we discuss LHP NCs historical and current research pursuits, challenges in applications, and the related present and future mitigation strategies explored.