In this presentation we discuss a full (15D) quantum simulation of the infrared absorption spectrum and dynamics of the protonated water dimer (H5O2+) by the multiconfiguration time-dependent Hartree (MCTDH) method. The main features of the IR spectrum are explained an assigned, in particular a complicated doublet structure at about 1000 cm-1 related to the proton transfer motion, which was not understood. Also the couplings of various fundamental motions which shape the spectrum between 800 and 2000 cm-1 are explained and assigned. A picture of the cation arises in which the central proton motion determines the dynamics of various other modes, mostly water bending and water pyramidalization. We show that a full quantum-dynamical description of such a complex molecular system can be achieved, providing explicative and predictive power and a very good agreement to available experimental data. This success is largely due to the use of the MCTDH method, a powerful algorithm for propagating wavepackets. The basics of the MCTDH algorithm are briefly discussed. To account for the interatomic potential and the interaction with the radiation we make use of the potential energy surface and dipole-moment surfaces recently developed by Bowman and collaborators, which constitute the most accurate ab initio surfaces available to date for this system.