While changes in the long-term mean state of climate will have many important consequences on a range of environmental, social, and economic sectors, the most significant impacts of climatic change are likely be generated by shifts in the intensity and frequency of extreme weather events. Indeed, insurance costs resulting from extreme weather events have been steadily rising since the 1970s, essentially in response to increases in population pressures in regions that are at risk, but also in part because of recent changes in the frequency and severity of certain forms of extremes. Regions now safe from catastrophic wind storms, heat waves, and floods could suddenly become vulnerable in the future. Under such circumstances, the associated damage costs could be extremely high. This paper provides an overview of certain climate extremes that have generated in recent years very costly impacts in the Swiss Alps, namely heat waves and strong convective precipitation, and how these events may change as climate warms in response to increased greenhouse-gas concentrations.