The Belle II experiment at the SuperKEKB $B$-factory at KEK is expected to start collecting data at the beginning of 2018, opening a new era for collider physics. Complementary to the LHC experiments, Belle II is designed to explore the intensity frontier. Its target is to collect an integrated luminosity of 50 ab$^{-1}$ by 2024, which is 50 times larger than the data sample recorded by the Belle experiment. The Belle II data will offer a unique possibility of searching for New Physics phenomena through precision study of rare and suppressed processes, as well as further revealing the nature of QCD in describing matter. The physics program of Belle II will be wide and only a selection of topics are highlighted in this paper: semileptonic and leptonic $B$ decays, electroweak penguins decays, time-dependent CP-violating decays, studies of mixing and rare decays in the charm sector, lepton flavour violation in $\tau$ decays, opportunities in bottomonium physics and searches for the dark sector.