Modern ideas coming from dynamical systems theory and statistical mechanics allow for a much-improved understanding of the relationship between climate variability and climate response to to forcings. This is also leading to the possibility of finding a synthesis between Hasselmann and Lorenz’s visions of climate, the first based on stochasticity, the latter rooted in deterministic chaos. I will focus on the global stability properties of the climate, and specifically on the dichotomy between the co-existing warm and snowball states, which has had a key importance for the development of life. When stochastic forcing is included, one observes transitions between the competing basins of attraction. For weak Gaussian noise laws, large deviation laws define the invariant measure, the statistics of escape times, and typical escape paths called instantons. The Melancholia state, the chaotic saddle embedded in the boundary between the basins of attraction, is the gateway for noise-induced transitions. The metastability can be understood in terms of an energy-like landscape with valleys and mountain ridges defined by the Graham's quasipotential. Finally, I will discuss generalizations of these results due to the presence of a larger number of competing states and on the consideration of other classes of noise laws and will discuss how data driven methods can help identifying non-trivial metastable states. Refs:Lucarini, T. Bodai, Transitions across Melancholia States in a Climate Model: Reconciling the Deterministic and Stochastic Points of View, Phys. Rev. Lett. 122,158701 (2019)Lucarini, T. Bodai, Global Stability Properties of the Climate: Melancholia States, Invariant Measures, and Phase Transitions, Nonlinearity 33, R59 (2020)Margazoglou, T. Grafke, A. Laio, V. Lucarini, Dynamical Landscape and Multistability of the Earth's Climate, Proc. R. Soc. A 477, 2021001920210019 (2021)Lucarini, L. Serdukova, L., and G. Margazoglou, Lévy-noise versus Gaussian-noise-induced Transitions in the Ghil-Sellers Energy Balance Model, Nonlin. Processes Geophys. https://doi.org/10.5194/npg-2021-34 (2022)Ragon, V. Lembo, V. Lucarini, C. Verard, J, Kasparian, M. Brunetti, Robustness of competing climatic states, J. Climate 35, 2769-2784 (2022)