This thesis is devoted to a theoretical study of high-temperature superconductivity from the viewpoint of a doped Mott insulator. To this end, the square-lattice t-J model is analyzed by variational and mean-field approaches. The thesis focuses on the construction of excitations and on spectral properties in the framework of Anderson's concept of resonating-valence-bond wavefunctions. The quantum dimer model as a toy model for the resonating-valence-bond phase of Mott insulators is also explored. In the first part of the thesis, the single-particle Green's functions in the superconducting phase are analyzed using Gutzwiller-projected variational wavefunctions for the t-J model. It is found that the overall spectral weight is reduced by a momentum-dependent renormalization, and that the projection produces a particle-hole asymmetry in the renormalization of the spectral weights. The second part analyzes the Green's functions in the pseudogap phase of the cuprates within an SU(2) mean-field approach where the order parameter fluctuates between the d-wave superconductor and the non-superconducting staggered-flux state. The model predicts a photoemission spectrum with an asymmetric gap structure interpolating between the superconducting gap centered at the Fermi energy and the asymmetric staggered-flux gap. This gap asymmetry changes sign at the "hot-spots" where the Fermi surface crosses the diagonal (0,π)-(π,0). In the last part of the thesis, single hole and vortex excitations in the liquid phase of the triangular-lattice Rokhsar-Kivelson quantum dimer model are considered. It is found that the motion of a hole bound to a topological excitation is strongly constrained due to interference effects.