The dynamics of a typical open quantum system, namely a quantum Brownian particle in a harmonic potential, is studied focusing on its non-Markovian regime. Both an analytic approach and a stochastic wavefunction approach are used to describe the exact time evolution of the system. The border between two very different dynamical regimes, the Lindblad and non-Lindblad regimes, is identified and the relevant physical variables governing the passage from one regime to the other are singled out. The non-Markovian short-time dynamics is studied in detail by looking at the mean energy, the squeezing, the Mandel parameter, and the Wigner function of the system.