Creating an effective carbon management system has become an urgent necessity to combat climate change. In the context of carbon farming, a set of sustainable agricultural practices is employed to sequester atmospheric carbon dioxide. These practices include methods like crop rotation, agroforestry, and conservation tillage. All of these practices help to capture and store carbon in the soil and plant biomass. However, the effectiveness and success of these initiatives rely on accurate and precise monitoring, as well as secure and transparent data management. Traditional centralized carbon credit verification systems are inefficient, vulnerable to fraud, and prone to errors, which limits their ability to verify the authenticity and reliability of carbon credits. A promising solution to solve this challenge involves combining Blockchain technology with the Internet of Things (IoT) to enable real-time data collection, transparent record-keeping, and tamper-proof validation of carbon sequestration efforts. This paper provides a comprehensive study of Blockchain-IoT-based carbon management systems, highlighting their potential benefits and limitations. It also addresses key challenges, explores future opportunities, and concludes with recommendations for future work in this area.