  Randomised measurements provide a way of determining physical quantities
without the need for a shared reference frame nor calibration of measurement
devices. Therefore, they naturally emerge in situations such as benchmarking of
quantum properties in the context of quantum communication and computation
where it is difficult to keep local reference frames aligned. In this review,
we present the advancements made in utilising such measurements in various
quantum information problems focusing on quantum entanglement and Bell
inequalities. We describe how to detect and characterise various forms of
entanglement, including genuine multipartite entanglement and bound
entanglement. Bell inequalities are discussed to be typically violated even
with randomised measurements, especially for a growing number of particles and
settings. Additionally, we provide an overview of estimating other relevant
nonlinear functions of a quantum state or performing shadow tomography from
randomised measurements. Throughout the review, we complement the description
of theoretical ideas by explaining key experiments.
