Climate tipping elements are large-scale subsystems of the Earth that may transgress critical thresholds (tipping points) under ongoing global warming, with substantial impacts on the biosphere and human societies. Frequently studied examples of such tipping elements include the Greenland Ice Sheet, the Atlantic Meridional Overturning Circulation (AMOC), permafrost, monsoon systems, and the Amazon rainforest. While recent scientific efforts have improved our knowledge about individual tipping elements, the interactions between them are less well understood. Also, the potential of individual tipping events to induce additional tipping elsewhere or stabilize other tipping elements is largely unknown. Here, we map out the current state of the literature on the interactions between climate tipping elements and review the influences between them. To do so, we gathered evidence from model simulations, observations, and conceptual understanding, as well as examples of paleoclimate reconstructions where multi-component or spatially propagating transitions were potentially at play. While uncertainties are large, we find indications that many of the interactions between tipping elements are destabilizing. Therefore, we conclude that tipping elements should not only be studied in isolation, but also more emphasis has to be put on potential interactions. This means that tipping cascades cannot be ruled out on centennial to millennial timescales at global warming levels between 1.5 and 2.0 ∘C or on shorter timescales if global warming surpassed 2.0 ∘C. At these higher levels of global warming, tipping cascades may then include fast tipping elements such as the AMOC or the Amazon rainforest. To address crucial knowledge gaps in tipping element interactions, we propose four strategies combining observation-based approaches, Earth system modeling expertise, computational advances, and expert knowledge.