It is a well-known issue that the 2050 target of carbon emissions neutrality will be reached only with the co-operation of all the interested sectors, and the construction sector could be one of the main contributors to this change. With the built environment globally responsible for about 40% of annual global energy-related CO2 emissions, the construction sector offers an important opportunity to drive transformative change and presents the most challenging mitigation potential among all industrial sectors, which also brings opportunities for adopting sustainability practices and increasing resilience. This paper presents a systematic literature review of those two pivotal concepts to reach the decarbonization goal: sustainability and resilience. Starting from an extensive literature review (2536 scientific documents) based on the PRISMA statement, the definitions and assessment methodologies of those concepts for the construction sector have been studied. The methodological approach followed for their analysis has been conducted on a first selection of 42 documents, further reduced to 12 by using clear inclusion criteria to identify the integrated assessment procedures. The main goal of this study is to clarify the correlation between sustainability and resilience concepts for constructions and their integrated assessment, in line with the latest regulations and market needs. The results show that, currently, sustainability and resilience are mainly evaluated in a distinct way to obtain building energy performance certificates, as well as to quantify the building market value and its complementary contribution to the ‘energy efficiency first’ principle and energy-saving targets towards the emergent issue of climate change. Few works focus on the integrated assessment of both concepts considering the construction industries’ point of view about materials and/or systems for buildings. The novelty of this study is the critical review of the current sustainability and resilience integrated assessment methods used for the construction value chain, declined for four main target groups. Researchers, policymakers, industries, and professionals could gain dedicated insights and practical suggestions to put in practice the elements of circular economy, ecological innovation, and cleaner production, which are essential in order to drive the decarbonization of the built environment.