The ultra rare kaon decay $K\rightarrow \pi \nu \bar{\nu}$, being one of the theoretically cleanest meson decays, is very sensitive to the effects of New Physics at high mass scales. NA62 is a fixed-target experiment at the CERN SPS designed to measure the branching ratio of the $K^{+}\rightarrow \pi^{+} \nu \bar{\nu}$ decay with 10% precision using a novel decay-in-flight technique. NA62 took data during run periods in 2016, 2017 and 2018. The results from the analysis of the data collected by NA62 in 2016, corresponding to $(1.21 \pm 0.04_{syst}) \times 10^{11}$ $K^{+}$ decays (2% of full available statistics), will be presented and future prospects will be reviewed. Although NA62 was designed to measure $K\rightarrow \pi \nu \bar{\nu}$, it's also sensitive to other rare and forbidden kaon decays, especially those with two leptons in the final state. The status and prospects of searches for lepton flavour and lepton number violation in kaon decays at the NA62 experiment will also be discussed.