Recent breakthroughs have led to creating true quantum states of solid-state mechanical objects. In the project we develop new protocols for sensing that make use of the unique quantum-mechanical properties of mechanical oscillators. For the purpose, we use different realizations in cavity optomechanics, quantum acoustics with superconducting qubits, and nano-electro-mechanics. While quantum limits to noise and sensitivity have long been an important consideration in laboratory tests of some mechanical sensors, our proposal aims to make use of distinctly quantum properties such as non-Gaussianity, multi-mode entanglement, and single-phonon nonlinearities to enhance the performance of these systems. In other words, analogously to what has long been done in atomic or spin-based sensors, we will explore using quantum states as a new resource for enhancing the capabilities of mechanical sensors.