This thesis addresses the problem of nuclear quantum dynamics and focuses on trajectory-based methods, in the context of the computation of quantum vibration spectra of large condensed-phase systems. We introduce a new approximation to the Wigner thermal density based on the Edgeworth expansion which is not subject to the oscillating sign problem and show that it performs better than its most common alternatives. We use this approximation to compute time correlation functions (TCFs) in the context of linearized semi-classical initial value representation. We also introduce an original Langevin dynamics, the Wigner-Langevin dynamics, that rigorously conserves the Edgeworth approximation and show that it can be used to compute approximate TCFs. In the second part of this thesis, we combine perturbative analysis with numerical calculations to examine the performance of different quasiclassical approaches to capture anharmonic spectral features (overtones, combination bands and Fermi resonances) in model systems of increasing complexity. Our results indicate that the intertwined effects of initial quantum sampling and propagation is non-trivial and that lack of coherence does not necessarily imply that trajectory-based methods are inherently (or equally) incapable of capturing finer spectral features. Finally, we assess the performance of the recently introduced adaptive Quantum Thermal Bath (adQTB) on liquid and solid water. We found that the adQTB largely increases the accuracy over the standard QTB, that it is in good agreement with path-integrals references for structural properties and yields infrared spectra comparable to state-of-the-art quasiclassical methods.