In this talk, we completely characterize the boundedness of composition operators with zero characteristic acting on the Hardy spaces of Dirichlet series $\mathscr{H}^p$ $(p>2)$, which resolves an open problem since the bounded composition operators on the Hilbert space of Dirichlet series were described by Gordon and Hedenmalm in 1999. Our strategy is completely different from what has been known so far. The characterization of compact composition operators generated by Dirichlet series symbols on $\mathscr{H}^p$ $(p\geq2)$ is also obtained.
