The frequent occurrence of geopolitical crises in the post-financial crisis era is driving the rethinking behind whether the global crude oil market is still a highly connected “great pool”. Using the spillover network model suggested by Baruník and Křehlík (2018), and the daily data of 31 global crude oil markets from 2009 to 2019, this study examines the return and volatility spillover effects and their time-varying behavior in six crude oil market segments at different timescales. The findings indicate that heterogeneity exists in the co-movements between global crude oil markets in the post-financial crisis era. In the medium term, both return and volatility spillover effects are not significant, which makes the diversified portfolio strategy useful. Prices in the Europe and Central Asian regions take the lead in return spillovers. In contrast, Asia-Pacific regional prices contribute the most in terms of volatility spillovers. Long-term volatility spillovers increase sharply when confronted with oil-related events in the post-financial crisis era. Therefore, policymakers should take effective measures to prevent any large-scale risk transmission in the long run.