Biomolecular recognition including binding of small molecules, peptides and proteins to their target receptors plays a key role in cellular function and has been targeted for therapeutic drug design. However, the high flexibility of biomolecules and slow binding and dissociation processes have presented challenges for computational modeling. Here, we review the challenges and computational approaches developed to characterize biomolecular binding, including molecular docking, Molecular Dynamics (MD) simulations (especially enhanced sampling) and Machine Learning. Further improvements are still needed in order to accurately and efficiently characterize binding structures, mechanisms, thermodynamics and kinetics of biomolecules in the future.