Greenhouse gas (GHG) emissions from buildings, particularly embodied carbon (EC), coupled with escalating construction costs, pose a dual challenge for achieving sustainable and affordable housing. While design decisions made during the early stages of a project strongly influence both EC and cost outcomes, existing research often addresses these aspects in isolation. This paper presents a systematic literature review (SLR) examining the significance of building design optimisation (BDO) in simultaneously reducing embodied carbon and construction costs. The review was conducted following PRISMA guidelines, drawing on publications from Scopus. Findings revealed that, building design optimisation is a key approach of reducing EC emissions and construction costs of the buildings. Further, it was discussed various tools and software adopted for building design optimisation research studies with pros and cons of each identified optimisation tool to provide as a guidance for selecting design optimisation method for future research studies. The findings of the study revealed that, BDO adopted for upfront EC reduction and construction cost of residential buildings is fragmented. This study contributes theoretically by framing BDO as a dual lever for affordability and decarbonisation of buildings.