Recent advances in miniaturization and commercial availability of critical satellite subsystems and detector technology have made small satellites (SmallSats, including CubeSats) an attractive, low-cost potential solution for space weather research and operational needs. Motivated by the first International Workshop on SmallSats for Space Weather Research and Forecasting, held in Washington, DC on 1-4 August 2017, we discuss the need for advanced space weather measurement capabilities, driven by analyses from the World Meteorological Organization (WMO), and how SmallSats can efficiently fill these measurement gaps. We present some current, recent missions and proposed/upcoming mission concepts using SmallSats that enhance space weather research and provide prototyping pathways for future operational applications; how they relate to the WMO requirements; and what challenges remain to be overcome to meet the WMO goals and operational needs in the future. With additional investment from cognizant funding agencies worldwide, SmallSats—including standalone missions and constellations—could significantly enhance space weather research and, eventually, operations, by reducing costs and enabling new measurements not feasible from traditional, large, monolithic missions.