Single-molecule magnets (SMMs) have been proposed for applications in high-density storage, quantum simulation, quantum computing and spintronics applications. Bulk magnetometric and spectroscopic techniques of molecular systems have allowed the observation of remarkable quantum effects in SMMs, such as the observation of an energy barrier, the reversal of the magnetization and quantum tunnelling of the magnetization. Over the past 10 years, scanning tunnelling microscopy of SMMs and single-molecule devices architectures, such as spin valves and spin transistors, have shed light onto the quantum properties of SMMs at the single-molecule level. More recently, new techniques, where the spin degrees of freedom in SMMs can be read out by photons, are being studied. Here, we review key techniques allowing the observation of quantum effects, important for the initialization, control and readout of the states of the SMMs, ultimately leading to the implementation of SMMs in technological applications.