Inadequate access to electricity impedes improvements in human living standards. Cheaper low-carbon technologies enable electricity access using decentralised off-grid systems; however, the financial sustainability of such systems remains challenging. Nevertheless, renewables-based off-grid systems may be the cheapest and most reliable electricity access option for some users. In this thesis, I develop an existing energy system model and present a new geospatial model, both of which are open-source. Using these tools, I investigate economic challenges facing off-grid electricity access. Firstly, I use energy systems modelling to explore electricity supply options for healthcare and domestic use in India. I find that the grid is unreliable and that solar-based mini-grids are normally cheaper than diesel-based ones. Adding healthcare-based demand to domestic demand reduces the cost of mini-grid electricity and enhances financial sustainability. Secondly, I extend an existing energy systems model to simulate hybrid solar mini-grids with dispatched diesel generation. I then apply this model to a humanitarian setting and demonstrate the potential for reducing costs by optimising the operational strategy. Additionally, I explore the impacts of adding new consumers to the system, demonstrating that whilst surplus solar electricity limits additional costs at lower levels, at higher levels fuel costs may be a financial burden. Finally, I present a new geospatial tool for investigating least-cost electricity access pathways. I use this tool to examine pathways to universal household electricity access in Sub-Saharan Africa under different demand, reliability, and carbon price scenarios. The results suggest that higher demand levels necessitate greater investment in grid extension and that applying a financial penalty for unmet demand or a carbon price increases the share of off-grid solar used in least-cost pathways. Together, these investigations quantify the extent to which low-carbon off-grid systems can become more economically attractive in the drive towards increased electricity access.