Paleoclimate information has played an instrumental role in showing how fast climate can vary and how large these changes can be. It provided the first vivid demonstration of the relationships between atmospheric greenhouse gas concentrations and surface air temperatures, as well as striking representations of climate change impacts and possible feedbacks within the climate system, such as those associated with vegetation or ice sheet changes. Here, a short review of recent advances in paleoclimate studies is provided, with the objective of showing what this information on past climates and environments can bring to research on current and possible future climates. We advocate that 1) paleoclimatic and paleoenvironmental information can be leveraged for narratives about climate change, in particular at the local and regional levels, 2) paleoclimate data is essential for out-of-range tests of climate models, since future climates are also out of the range of recent climate information used for calibrating climate models, 3) paleoclimate data, in particular for the last millennia, is essential for taking multi-centennial and multi-millennial variability into account when describing trends related to anthropogenic forcings and attributing climate change signals, in particular for extreme and rare events, and 4) paleoclimates also provide extremely valuable information for initializing the slow components of climate models. In addition, we show how paleoclimate studies can be beneficial to put recent and future climate change into context and improve our knowledge on key processes. They can both benefit from and contribute to models and knowledge based on the study of recent and future climates.