The algorithm of Equilibrium Propagation (EP) 1 is highly interesting for training physical systems as it extracts backprop-equivalent gradients directly from their convergence to a steady state 2,3. In my talk, I will show that it is an excellent starting point for building and training physical systems to perform classification tasks. I will first describe how we have used EP to train the hardware D-Wave Ising machine in a supervised way to recognize handwritten digits 4. I will then show that EP can unlock self-learning in spiking neural networks 5. Finally, I will explain how we can extend EP to unsupervised learning.