A valence-bond solid is a quantum paramagnetic phase that can be realized in a quantum spin system,  characterized by the absence of magnetic long-range order, but broken lattice symmetries. The elementary excitations of a dimerized VBS phase correspond to singlets turned into triplets,  the so-called triplons. Such excitations can be analytically described  within the bond-operator representation, where spin operators are expanded in terms of singlet and triplet boson operators. In this talk, we will discussed the stability and properties of  many-triplon states.  We will concentrate on the intermediate parameter region of the square lattice spin-1/2  J1--J2 antiferromagnetic Heisenberg model, where a quantum paramagnetic phase sets in. An introduction to the model, valence-bond solid phases, and the bond-operator formalism will be presented.  We will show our mean-field results for the excitation spectrum above a many-triplon state, in addition to spin-spin and dimer-dimer correlation functions, dimer order parameters,  and the bipartite von Neumann entanglement entropy as a function of the triplon number. We also comment on possible relations between many-triplon states with large triplon number and gapped spin-liquid states.