Over the past decade, governments have introduced increasingly stringent climate policies to curb emissions in line with Paris Agreement targets. However, broad carbon-pricing schemes, although effective at reducing emissions, can potentially impose disproportionate burdens on underserved communities. Drawing on recent global distributional evidence, we frame this tension by documenting a shift in global carbon inequality from between-country to within-country disparities (the inter-country share declining from 62% in 1990 to 36% in 2019), alongside the persistently outsized contribution of the top 10% of emitters. We then extend the analysis to residential energy consumption using a global panel of 180 countries (1990-2023), showing that inequality in household energy consumption is substantial but lower than income inequality (global Gini: 0.401 vs. 0.636; Theil: 0.263 vs. 0.720). The geography of these disparities remains structurally patterned: Europe and Eastern Europe, along with the Commonwealth of Independent States, account for nearly 90% of the between-region component of global residential-energy inequality, whereas Developing Asia exhibits the largest within-region dispersion. Without clear, comparable metrics to judge whether policies meet minimum energy requirements, reconciling mitigation with equitable access is set to remain a considerable challenge.