DC distribution systems (DCDSs) are a promising alternative to AC systems because they remove AC-DC conversions between renewable sources and loads. Their unique features compared to AC include low system inertia, strict power limits and power–voltage coupling. In a liberalised electricity market, merely applying an AC market design to a DCDS cannot guarantee the latter’s supply security and voltage stability; new markets must be designed to meet DC challenges. This article identifies the key design options of DCDS electricity markets. To identify these options, we develop a comprehensive design framework for local electricity markets; to our knowledge, we provide the first such analysis. Whereas previous studies focus on separate aspects of DCDS markets, we widen the scope to include the role of market architecture and investigate the arrangements of sub-markets. As an illustration, we demonstrate three promising DCDS market designs that can be defined in our framework, and provide a first assessment of their performance.