Recent successes in deep learning for vision and natural language processing are attributed to larger models but come with energy consumption and scalability issues. Current training of digital deep-learning models primarily relies on backpropagation that is unsuitable for physical implementation. In this work, we propose a simple deep neural network architecture augmented by a physical local learning (PhyLL) algorithm, which enables supervised and unsupervised training of deep physical neural networks without detailed knowledge of the nonlinear physical layer’s properties. We trained diverse wave-based physical neural networks in vowel and image classification experiments, showcasing the universality of our approach. Our method shows advantages over other hardware-aware training schemes by improving training speed, enhancing robustness, and reducing power consumption by eliminating the need for system modeling and thus decreasing digital computation. Editor’s summary The recent development of large-scale deep neural networks (NNs) and other artificial intelligence (AI) applications is accompanied by growing concerns about the energy consumption needed to train and operate them. Physical NNs could become a solution to this problem, but the direct hardware implementation of conventional algorithms faces multiple difficulties. For instance, training NNs using conventional backpropagation algorithms is associated with challenges such as lack of scalability, complexity of operation during training, and dependency on digitally trained models. Inspired by the forward-forward algorithm, Momeni et al. report the practical demonstration of backpropagation-free training of wave-based physical NNs. Their work is an important step in optimizing the energy-intensive training step in NNs for more efficient solutions for modern AI systems. —Yury Suleymanov Wave-based physical neural networks were trained without backpropagation using a forward-forward algorithm.