Collective magnetic excitations are a fascinating aspect of condensed matter physics, where neutron scattering can provide valuable insight into the magnetic properties of physical realisations of model systems. This thesis focuses on the excitation spectra of layered quantum magnets in the case of the frustrated quantum magnet SrCu$_2$(BO$_3$)$_2$ and the family of quasi-2D antiferromagnets MPS$_3$, with M a transition metal. \begin{itemize}[topsep=2pt,itemsep=-0.7ex] \item SrCu$_2$(BO$_3$)$_2$ is a physical realisation of the two-dimensional Shastry-Sutherland theoretical model, constructed as orthogonal dimers with the product of singlets on the strong antiferromagnetic $J$ bond as an exact ground state. The spin interactions for such a particular geometry induces strong frustration which leads to unconventional magnetism and exotic phases of matter. This work is concerned with a series of aspects of the magnetic excitations in this compound. The excitation spectra as a function of field, temperature and pressure are measured using neutron time-of-flight spectroscopy. The experimental results show that correlations, bound magnons and finite temperature properties are highly unconventional and these results are compared with existing theories on frustrated model systems. In addition, predicted topological properties of SrCu$_2$(BO$_3$)$_2$ in an applied field are confirmed experimentally. \item The transition metal phosphorus trisulfides (MPS$_3$) are a family of quasi two-dimensional materials on a honeycomb lattice with weakly bound magnetic planes. This work focuses mainly on the exchange interactions and critical properties of FePS$_3$, which is largely anisotropic with the S=2 Fe$^{2+}$ moments pointing normal to the $(a,b)$ plane. Inelastic neutron scattering on single crystals is used to measure the spin wave dispersion, providing new insight on the strength of the coupling interactions and anisotropies and showing that FePS$_3$ is a good two-dimensional model antiferromagnet. Similar experiments on powdered samples of NiPS$_3$ show low-Q dispersive spin waves with a small spin-gap. Critical properties of FePS$_3$ close to the Néel temperature are further discussed, as the magnetic nature of the measured quasi-elastic scattering is confirmed. Based on magnetization measurements in high pulsed fields, a possible tricritical point in the 40-50T range is proposed. \end{itemize} The work presented in this thesis has been carried out in a collaboration between the Institut Laue Langevin in Grenoble and the Laboratory for Quantum Magnetism of the EPFL.