The asymptotic expansions to the Boltzmann equations provide a clue of the connection from kinetic theory to fluid mechanics. The Hilbert expansion turns out to be useful to verify compressible fluid limits. As its applications, we rigorously establish the compressible Euler and acoustic limits from the Boltzmann equation and the Euler-Poisson limit from the Vlasov-Poisson-Boltzmann system. Moreover, we prove a global-in-time convergence for a repulsive Euler-Poisson flow for irrotational monatomic gas.