This paper introduces NequIP, a novel machine learning method for computing interatomic potentials and atomic forces of molecules and materials using E(3)-equivariant neural networks. NequIP employs E(3)-equivariant convolutions on geometric tensors, which capture more information-rich and faithful representations of atomic environments compared to invariant convolutions used in most contemporary symmetry-aware models. The method achieves state-of-the-art accuracy on a diverse set of molecules and materials while demonstrating remarkable data efficiency, requiring up to three orders of magnitude fewer training data compared to existing models. NequIP outperforms other models, including kernel-based approaches, on small molecular datasets and shows high-fidelity reproduction of structural and kinetic properties in molecular dynamics simulations. The high data efficiency of NequIP allows for the construction of accurate potentials using high-order quantum chemical reference calculations, enabling long-time scale molecular dynamics simulations. The paper also discusses the theoretical underpinnings of equivariance and its impact on learning dynamics, and highlights the potential benefits of explicitly including long-range interactions in deep learning interatomic potentials.This paper introduces NequIP, a novel machine learning method for computing interatomic potentials and atomic forces of molecules and materials using E(3)-equivariant neural networks. NequIP employs E(3)-equivariant convolutions on geometric tensors, which capture more information-rich and faithful representations of atomic environments compared to invariant convolutions used in most contemporary symmetry-aware models. The method achieves state-of-the-art accuracy on a diverse set of molecules and materials while demonstrating remarkable data efficiency, requiring up to three orders of magnitude fewer training data compared to existing models. NequIP outperforms other models, including kernel-based approaches, on small molecular datasets and shows high-fidelity reproduction of structural and kinetic properties in molecular dynamics simulations. The high data efficiency of NequIP allows for the construction of accurate potentials using high-order quantum chemical reference calculations, enabling long-time scale molecular dynamics simulations. The paper also discusses the theoretical underpinnings of equivariance and its impact on learning dynamics, and highlights the potential benefits of explicitly including long-range interactions in deep learning interatomic potentials.