||Kelvin−Helmholtz instability (KHI) and Raleigh−Taylor instability (RTI) are basic physical processes in fluids and magnetized plasmas, which are important for understanding many astrophysical phenomena and play a role in plasma heating. Solar jets are the plasma ejections along the open magnetic field lines in the solar corona. The differences in densities and flow speeds between an expanse of erupting plasma and the background plasma may trigger the RTI and KHI, if the stabilizing effects of the solar magnetic field are surpassed. We review the development of the theory and simulations about the instabilities in solar jets, and introduce the observations about the KHI and RTI in solar jets. Using high-resolution data from the Interface Region Imaging Spectrograph (IRIS), we report that two upward flows, with a strong velocity shear of 204 km/s, travelling parallel to each other, drive the onset of the KHI in a solar blow-out jet. Using the EUV data obtained from the Solar Dynamics Observatory (SDO), we observe that many vortex-like structures occur during the upstream and downstream regimes of the jets. Comparing the observations with the theoretical estimations, we suggest that the vortex-like structures in the upstream regime of the jet are manifestations of the KHI, and the vortex-like structures in the downstream regime are caused by both the RTI and KHI. Our finding extends evidently the range where the KHI and RTI take place in the solar atmosphere to much smaller scales, and implies that these instabilities may be rather ubiquitous on the Sun in the presence of jets.