Exceptional points (EPs), appearing in non-Hermitian systems as a specific class of spectral degeneracy at which the eigenvalues and eigevectors coalesce, have been extensively studied in the last decades due to their peculiar properties. In particular, around the EP, the spectral splitting scales sublinearly with the introduced perturbation, resulting in divergently increased signal responsivity. And due to its amplified response to perturbations, it may significantly exceed the sensitivity of traditional sensors. In the last decade, EP sensing has gone from theoretical conception to experimental implementation. Since the first experimental demonstration of improved signal responsivity in optical systems, EP sensing has made remarkable advances in achieving enhanced signal-to-noise ratio and measurement sensitivity, which are key parameters characterizing the sensing performance. In this paper, we first briefly introduce the history of EPs and the physical mechanisms underlying their enhanced sensing capabilities. We then review the current status of EP sensing, including the improvements in signal sensitivity, signal-to-noise ratio, and measurement sensitivity on various physical platforms including optical, mechanical, and quantum systems. Afterwards, the main challenges faced by EP sensing including noise amplification and system stability are discussed. Finally, we point out possible solutions to address these limitations by using quantum effects such as quantum squeezing, and outline potential future development directions.