This paper provides a review of the economics of tipping points in natural resources and climate change economics, examining recent advances in theoretical modeling and controlled experiments. We begin with the non-convexity models as a theoretical foundation, provide a typology of the resulting deterministic tipping points, and discuss their implications for management. Then, we focus on hazard rate modeling for optimal resource management with stochastic and unknown tipping points. We discuss Bayesian learning, strategic behavior among agents, and the advancement in integrated assessment modeling with multiple and interacting tipping points. Finally, we examine the new contributions of experimental economics to understanding decision-making processes in the presence of tipping points. The paper concludes by highlighting the main advances in the literature and outlining future research directions, ultimately aiming to encourage further investigation and the development of innovative tools to address global challenges.