The construction project success factors in India as well as globally are broadly measured in terms of their performance against cost, time, quality, and safety parameters. However, the impacts of these projects in long term on the society and environment are majorly ignored in previous times which caused global rise in temperature and inevitable necessity to adopt net-zero initiatives and associated sustainable construction practices in the construction industry globally. However, introduction of sustainable construction practices and associated changes to the already established construction practices in the industry is laborious and time-consuming. In addition, it is more difficult if the new sustainable practices negatively affect the perceived project success factors like time, cost, and quality. This is the current scenario of the sustainable practices as they are time-consuming due to less infrastructure and non-cost-effective and quality is not time-tested. This literature review paper aims to identify the challenges to adopt the sustainable practices in the current scenario of the construction industry in India and worldwide which pulls back from the low carbon construction and net-zero targets. To identify the challenges, the citation analysis of bibliometric research is conducted and relevant papers are identified from 2005 to 2023. The challenges and its solutions are segregated from these papers and presented. The major challenges include lack of knowledge, higher costs and its unequal distributions, immature green supply chain system, social challenges due to unawareness of public, and non-appropriate regulations. The major solutions identified from review are adoption of new technologies like off-site manufacturing and prefabrication, adoption of lean principles: 3Rs (Reuse, Reduce, Recycle) and evolution of circular economies, adoption of integrated building designs for design of high-performance buildings, trainings for public awareness and sustainability-based skills development to the practicing engineers, further legislations and government incentives to adopt the sustainable practices, etc. Accepting these challenges assimilated from the various studies globally and adopting the solutions proposed can marginally improve the Sustainability Development Goals (SDGs) of the country. Since the sustainability practices in buildings and construction sector are evolving, this study suggests the following potential areas for future research: the quality of sustainable materials through various tests, further development of new technologies, adoption of various policies and legislation to improve sustainability, and green supply chain management evolution.