Solid-state electrolytes (SSEs) have emerged as high-priority materials for safe, energy-dense and reversible storage of electrochemical energy in batteries. In this Review, we assess recent progress in the design, synthesis and analysis of SSEs, and identify key failure modes, performance limitations and design concepts for creating SSEs to meet requirements for practical applications. We provide an overview of the development and characteristics of SSEs, followed by analysis of ion transport in the bulk and at interfaces based on different single-valent (Li+, Na+, K+) and multivalent (Mg2+, Zn2+, Ca2+, Al3+) cation carriers of contemporary interest. We analyse the progress in overcoming issues associated with the poor ionic conductivity and high interfacial resistance of inorganic SSEs and the poor oxidative stability and cation transference numbers of polymer SSEs. Perspectives are provided on the design requirements for future generations of SSEs, with a focus on the chemical, geometric, mechanical, electrochemical and interfacial transport features required to accelerate progress towards practical solid-state batteries in which metals are paired with energetic cathode chemistries, including Ni-rich and Li-rich intercalating materials, sustainable organic materials, S8, O2 and CO2.