∼6% of all known pulsars have been observed to exhibit sudden spin-up events, known as glitches. For more than fifty years, these phenomena have played an important role in helping to understand pulsar (astro)physics. Based on the review of pulsar glitches search method, the progress made in observations in recent years is summarized, including the achievements obtained by Chinese telescopes. Glitching pulsars demonstrate great diversity of behaviours, which can be broadly classified into four categories: normal glitches, slow glitches, glitches with delayed spin-ups, and anti-glitches. The main models of glitches that have been proposed are reviewed and their implications for neutron star structure are critically examined regarding our current understanding. Furthermore, the correlations between glitches and emission changes, which suggest that magnetospheric state-change is linked to the pulsar-intrinsic processes, are also described and discussed in some detail.