Bound-states of particles are an interesting problem in quantum mechanics dating back to 1931 Bethe's solution of spin-1/2 Heisenberg chain. These exotic composite states are realized in quantum magnets and are detectable in inelastic neutron scattering (INS) experiments. In this thesis, with the help of recent advances in matrix-product-states based algorithms, we numerically determine the Dynamical Structure Factor (DSF) to study the dynamics and spectrum of underlying spin models. We demonstrate the bound-states in three scenarios of quantum magnetism - (a) one dimensional Heisenberg ferromagnet where by studying temperature dependence of DSF we show that the bound-states appear as a well-defined excitation in temperature ranges J/12 <= T <= J/3, pointing to the possibility of its direct detection with INS experiments, (b) spin-1/2 ladders close to magnetic-field induced phase transition where high-energy mode-splits observed in INS experiments on (C5H12N)2CuBr4 (BPCB) are shown to be bound-states of triplets by zero temperature simulations on the frustrated ladder. Upon decreasing the frustration, the well-defined bound-state modes evolves into the observed split-feature in spin ladder, (c) the Shastry Sutherland compound SrCu2(BO3)2 in magnetic field, where INS experiments conducted at high-fields up to the onset of 1/8-magnetization plateau (at 27 T) and our zero-temperature numerical simulations on the adapted spin-model indicate a condensation of the spin-2 bound-state of triplets at 21 T, resulting in a field-induced spin-nematic phase.