The need to adequately compensate for damage to interests, especially of a non-pecuniary nature, caused by reckless behaviour towards climate change is now unavoidable. This is known as climate change damages. The consequences will be felt in time and space by younger and future generations. It is right to speak of damage that affect the existential legal sphere of individuals who are a priori determinable, for whom it is unthinkable to continue to invoke the unpredictability of the events that caused them. A punitive compensation may (also) prove to be the appropriate remedy, since it is at the same time: dissuasive, to prevent the continuation of prejudicial behaviour from the point of view of intergenerational solidarity; exemplary, to create an appropriate cultural sensitivity to the issue; and functional, in the immediate future, to fully compensate the damage suffered.