Nitrogen vacancy (NV) centre quantum sensors provide unique opportunities in studying condensed matter systems, as they are quantitative, non-invasive, physically robust, offer nanoscale resolution and may be used across a wide range of temperatures. These properties have been exploited in recent years to obtain nanoscale resolution measurements of static magnetic fields arising from spin order and current flow in condensed matter systems. Compared with other nanoscale magnetic-field sensors, NV centres have the advantage that they can probe quantities that go beyond average magnetic fields. Leveraging techniques from magnetic resonance, NV centres can perform high-precision noise sensing and have given access to diverse systems, such as fluctuating electrical currents in simple metals and graphene, as well as magnetic dynamics in yttrium iron garnet. In this Technical Review, we provide an overview of NV sensing platforms and modalities and discuss the connections between specific NV measurements and important physical characteristics in condensed matter, such as correlation functions and order parameters, that are inaccessible by other techniques. We conclude with our perspectives on the new insights that may be opened up by NV sensing in condensed matter. Nitrogen vacancy centre quantum sensors are quantitative, non-invasive and physically robust probes of condensed matter systems that offer nanoscale resolution across a wide range of temperatures. This Technical Review discusses the connections between NV measurements and important physical characteristics in condensed matter. Nitrogen vacancy (NV) centres can probe static and dynamic fields in a momentum-resolved and frequency-resolved way across a wide range of temperatures, from cryogenic temperatures to 1,000 K, complementing existing nanoscale probes.Static fields can be quantitatively mapped with nanotesla sensitivity and nanometre spatial resolution using NV centres, diagnosing microscopic properties in magnetic materials, transport systems and superconductors, as well as in diamond anvil cells under extreme gigapascal pressures.NV centres can also be used to measure noise from dynamic systems in a tunable way, providing access to the spectral density of noise from DC to tens of gigahertz while using the NV-sample distance to probe the relevant length scales of system dynamics.Recent progress has been made in coherent NV-based noise measurements, in which measurements resolving transitions in the shape of the NV coherence decay or simultaneous measurements of many NV centres can provide new windows into dynamic systems.
