The European Spallation Source, ESS, will use a linear accelerator delivering a high intensity proton beam with an average beam power of 5 MW to the target station at 2.5 GeV in long pulses of 2.86 ms. The ESS LINAC will use two types of superconducting cavities, spoke resonators at low energy and elliptical cavities at high energies. The possibilities to upgrade to a higher power LINAC at fixed energy are considered. This paper will present a review of the superconducting LINAC design and the beam dynamics studies.