A low-carbon energy transition is essential for mitigating climate change, but can also cause energy justice and equity impacts on Black, Indigenous, and People of Color (BIPOC), low-income, and other frontline communities. Examples include exacerbating energy burden, inaccessibility and unaffordability of low-carbon energy and electric end-use technologies, property value loss and displacement from renewable energy siting, and unequal health benefits and employment losses from fossil fuel retirement. To avoid perpetuating historical and creating new injustices, an equitable and just energy transition will require careful planning and execution. To this end, measuring and evaluating the effects of existing and proposed programs and policies aimed at decarbonizing energy systems is critical. However, methods and metrics for evaluating equity effects vary across disciplines and transitions, making it challenging to identify effective evaluation strategies. This paper presents a comprehensive review of the equity implications of low-carbon energy transitions and identifies key metrics that have been used across disciplines to quantify energy injustices and equity impacts. We focus on four key low-carbon energy transitions: (1) renewable energy deployment; (2) fossil fuel infrastructure retirement; (3) transportation electrification; and (4) residential building decarbonization. We classify energy justice and equity metrics into the dimensions of health, access, and livelihood, and construct an analytical framework that supports policymakers, planners and other stakeholders in identifying important equity considerations and quantitatively evaluating the effects of decarbonization initiatives. While our framework can serve as a starting point for evaluating justice and equity impacts of energy transitions, further work is needed to address the limitations of existing metrics and additional evaluation methods will be critical to effect energy transitions that are truly equitable.