Hamiltonian learning is the problem of inferring the Hamiltonian of a system from measurement data. In this talk I will introduce the setting where the data consists of measurement outcomes obtained at different points in time and where the system of interest evolves according to the Schrödinger equation. I will introduce a scalable, machine-learning inspired approach to learning many-body Hamiltonians based on efficient quantum state representations in terms of matrix-product states. This approach is demonstrated on synthetic data where the parameters of a Heisenberg-type Hamiltonian are learned.