Are global incomes converging or diverging? Despite recent empirical evidence supporting the hypothesis of uncondi￾tional beta convergence, this paper argues that such findings overlook the stark reality facing the world’s poorest people. Many lower income countries, including those among the so-called “Bottom Billion,” continue to slip further behind the rest of the world, while the numbers of those living in extreme poverty are beginning to rise again after decades of decline. The paper explores how these contradictions can coexist and discusses the policy importance of looking beyond global average trends. The paper identifies three confusions that can arise when analyzing trends in income convergence. First, a focus on unconditional convergence can overlook important policy questions, such as whether countries are likely to eradicate extreme poverty or to catch up with the rest of the world. Tests for convergence may yield only partial answers, especially in light of recent findings that show that unconditional beta convergence can coexist with a significant group of countries slipping ever further behind the rest of the world. Meanwhile extreme poverty numbers are increasing rather than decreasing. Second, average trends can both obscure and be distorted by underlying differences in country composition. In the extreme case, while fast-growing China was below global mean incomes between 2000 and 2020, it significantly boosted empirical support for global convergence. Now that China has passed this threshold, the finding will likely reverse in the coming years as more data is available. Third, different levels of availability of time periods and country coverage can distort and even bias empirical findings, espe￾cially where limitations to data availability is correlated with lower income or diverging economies.