Atomistic simulation based on quantum mechanics (QM) is currently being revolutionized by machine-learning (ML) methods. Many existing approaches use ML to predict molecular properties from quantum chemical calculations. This has enabled molecular property prediction within vast chemical compound spaces and the high-dimensional parametrization of energy landscapes for the efficient molecular simulation of measurable observables. However, as all properties derive from the QM wave function, an ML model that is able to predict the wave function also has the potential to predict all other molecular properties. In this talk, I will explore ML approaches that directly represent wave functions and QM Hamiltonians and their derivatives for developing methods that use ML and QM in synergy. Using example systems from heterogeneous catalysis and organic electronics, I will discuss the challenges associated with encoding physical symmetries and invariance properties into deep learning models of molecular electronic structure. Upon overcoming these challenges, integrated ML-QM methods offer the combined benefits of big-data-driven parametrization and first-principles-based methods. I will discuss several opportunities associated with building ML-augmented quantum chemical methods, including Inverse Chemical Design based on ML-predicted wave functions and the development of efficient and accurate surrogate models to study materials chemistry.