The effect of climate change on tropical cyclone intensity has been an important scientific issue for a few decades. Although theory and modeling suggest the intensification of tropical cyclones in a warming climate, there are uncertainties in the assessed and projected responses of tropical cyclone intensity to climate change. While a few comprehensive reviews have already provided an assessment of the effect of climate change on tropical cyclone activity including tropical cyclone intensity, this review focuses mainly on the understanding of the effect of climate change on basin-wide tropical cyclone intensity, including indices for basin-wide tropical cyclone intensity, historical datasets used for intensity trend detection, environmental control of tropical cyclone intensity, detection and simulation of tropical cyclone intensity change, and some issues on the assessment of the effect of climate change on tropical cyclone intensity. In addition to the uncertainty in the historical datasets, intertwined natural variabilities, the considerable model bias in the projected large-scale environment, and poorly simulated inner-core structures of tropical cyclones, it is suggested that factors controlling the basin-wide intensity can be different from individual tropical cyclones since the assessment of the effect of climate change treats tropical cyclones in a basin as a whole.