The synergistic combination of deep learning models and Earth observation promises significant advances to support the sustainable development goals (SDGs). New developments and a plethora of applications are already changing the way humanity will face the living planet challenges. This paper reviews current deep learning approaches for Earth observation data, along with their application towards monitoring and achieving the SDGs most impacted by the rapid development of deep learning in Earth observation. We systematically review case studies to 1) achieve zero hunger, 2) sustainable cities, 3) deliver tenure security, 4) mitigate and adapt to climate change, and 5) preserve biodiversity. Important societal, economic and environmental implications are concerned. Exciting times ahead are coming where algorithms and Earth data can help in our endeavor to address the climate crisis and support more sustainable development.