Beta-lactamase enzymes mediate the most common forms of gram-negative antibiotic resistance affecting clinical treatment. They also constitute an excellent model system for the difficult problem of understanding how allosteric mutations can augment catalytic activity of already-competent enzymes. Multiple allosteric mutations have been identified that alter catalytic activity or drug-resistance spectrum in class A beta lactamases, but predicting these in advance continues to be challenging. Here, we review computational techniques based on structure and/or molecular simulation to predict such mutations. Structure-based techniques have been particularly helpful in developing graph algorithms for analyzing critical residues in beta-lactamase function, while classical molecular simulation has recently shown the ability to prospectively predict allosteric mutations increasing beta-lactamase activity and drug resistance. These will ultimately achieve the greatest power when combined with simulation methods that model reactive chemistry to calculate activation free energies directly.