The use of quantum information promises many interesting applications, but these expectations can only be met with stringent levels of control of quantum devices. Efficient methods to ensure the correct functioning of these devices are therefore crucial for the development of quantum technologies. In this talk, I will discuss the certification of the output of quantum devices in the context of quantum information processing with infinite-dimensional Hilbert spaces, which stands as an interesting alternative to the use of finite-dimensional Hilbert spaces, notably for entanglement generation and error-correction. In that setting, quantum states are equivalently described by—and may be probed via—their phase-space representations. After introducing the beautiful mathematical formalism underlying the phase-space formulation of quantum mechanics, I will present efficient and robust methods for characterizing quantum states using phase-space measurements, a striking application being the efficient verification of Boson Sampling experiments.