The properties of mixtures of Bose-Einstein condensates at T=0 have been investigated using quantum Monte Carlo(QMC) methods and Density Functional Theory (DFT) with the aim of understanding physics beyond the mean-field theory in Bose-Bose mixtures. In particular, quantum liquid droplets with attractive intraspecies and repulsive interspecies attraction were studied, for which we observed significant contributions beyond Lee Huang Yang (LHY) theory that affect the energy, saturation density, and surface tension. The critical atom number in droplets in free space for total number of atoms N between N=30 and N =2000 was obtained. Results of the surface tension for three values of the attractive interspecies interactions are presented. For a homogeneous system, extensive calculations of the equations of state were performed and we report the influence of finite-range effects in beyond-Bogoliubov theory. In systems interacting with a small (large) effective range, we observe repulsive (attractive) beyond- LHY contributions to the energy. For the droplets in a mixture of 39^K atoms, which were observed experimentally for the first time, the calculations of equations of state were performed. Combining QMC-built functionals with DFT, the discrepancy in the estimation of critical atom number between the mean-field theory and experimental results was explained by the proper inclusion of the effective range in inter-particle interaction models. The influence of finite-range effects on breathing and quadrupole modes in 39^K quantum droplets was investigated. We predicted a significant deviation in the excitation frequencies when entering a more correlated regime. Finally, the phase diagram of repulsive Bose-Bose mixtures in a spherical harmonic trap using Quantum Monte Carlo calculations was studied. Density profiles were obtained reported, and we found the occurrence of three phases: separation of condensates in two blobs, fully mixed and shell-separated phase. A comparison with the Gross-Pitaevskii solutions showed a large deviation in the regime of large mass imbalance and strong interactions. We showed the universality in the density profiles with respect to the s-wave scattering length and found numerical evidence for Gross-Pitaevskii scaling present beyond the regime of applicability of Gross-Pitaevskii equations.