Nearly 40 % current global annual energy-related CO2 emissions come from the fossil fuel-dominated power sector. Accurately accounting for carbon emissions in power systems from the consumption-based perspective is crucial for achieving the low-carbon power transition. Consumption-based carbon accounting has emerged as a major research focus, which aids in the implementation of targeted measures such as low-carbon demand response and dispatch. Choosing an appropriate method to account carbon emission needs thorough consideration of characteristics of various methods. There still lacks a systematic review that concludes the essence and application status of these methods, as well as comparing their advantages and disadvantages. To address this gap, a consumption-based carbon accounting framework for power systems is proposed. This framework groups four typical methods into two perspectives: Attributional methods and consequential methods. The principles, calculation approaches, and research application status of these methods are comprehensively summarized in a transparent, integrated and comparative manner, which makes progress in two critical limitations: (i) temporal and spatial granularity, and (ii) consideration of the actual topology and operational constraints of the power grid. As improvements in the transparency and quality of electricity data and expansion of application scenarios, the flexibility and applicability of the framework will continue to improve to achieve the unity of efficiency and fairness. The proposed framework can serve as a valuable guide to conducting research and exploration on low-carbon energy management, policy and regulatory decisions and to inform the development of effective strategies for the low-carbon transition of power systems.