In recent years there has been a large scientific and public debate on climate change and its direct as well as indirect effects on human health. In particular, a large amount of research on the effects of climate changes on human health has addressed two fundamental questions. First, can historical data be of some help in revealing how short-run or long-run climate variations affect the occurrence of infectious diseases? Second, is it possible to build more accurate quantitative models which are capable of predicting the future effects of different climate conditions on the transmissibility of particularly dangerous infectious diseases? The primary goal of this paper is to review the most relevant contributions which have directly tackled those questions, both with respect to the effects of climate changes on the diffusion of non-infectious and infectious diseases, with malaria as a case study. Specific attention will be drawn on the methodological aspects of each study, which will be classified according to the type of quantitative model considered, namely time series models, panel data and spatial models, and non-statistical approaches. Since many different disciplines and approaches are involved, a broader view is necessary in order to provide a better understanding of the interactions between climate and health. In this respect, our paper also presents a critical summary of the recent literature related to more general aspects of the impacts of climate changes on human health, such as: the economics of climate change; how to manage the health effects of climate change; the establishment of Early Warning Systems for infectious diseases.