  Klaus Hasselmann's revolutionary intuition in climate science was to take
advantage of the stochasticity associated with fast weather processes to probe
the slow dynamics of the climate system. This has led to fundamentally new ways
to study the response of climate models to perturbations, and to perform
detection and attribution for climate change signals. Hasselmann's program has
been extremely influential in climate science and beyond. We first summarise
the main aspects of such a program using modern concepts and tools of
statistical physics and applied mathematics. We then provide an overview of
some promising scientific perspectives that might better clarify the science
behind the climate crisis and that stem from Hasselmann's ideas. We show how to
perform rigorous model reduction by constructing parametrizations in systems
that do not necessarily feature a time-scale separation between unresolved and
resolved processes. We propose a general framework for explaining the
relationship between climate variability and climate change, and for performing
climate change projections. This leads us seamlessly to explain some key
general aspects of climatic tipping points. Finally, we show that response
theory provides a solid framework supporting optimal fingerprinting methods for
detection and attribution.
