© 2018 Informa UK Limited, trading as Taylor & Francis Group. Understanding the thermal properties of disordered systems is of fundamental importance for condensed matter physics - and for practical applications as well. While quantities such as the thermal conductivity are usually well characterised experimentally, their microscopic origin is often largely unknown - hence the pressing need for molecular simulations. However, the time and length scales involved with thermal transport phenomena are typically well beyond the reach of ab initio calculations. On the other hand, many amorphous materials are characterised by a complex structure, which prevents the construction of classical interatomic potentials. One way to get past this deadlock is to harness machine-learning (ML) algorithms to build interatomic potentials: these can be nearly as computationally efficient as classical force fields while retaining much of the accuracy of first-principles calculations. Here, we discuss neural network potentials (NNPs) and Gaussian approximation potentials (GAPs), two popular ML frameworks. We review the work that has been devoted to investigate, via NNPs, the thermal properties of phase-change materials, systems widely used in non-volatile memories. In addition, we present recent results on the vibrational properties of amorphous carbon, studied via GAPs. In light of these results, we argue that ML-based potentials are among the best options available to further our understanding of the vibrational and thermal properties of complex amorphous solids.