Classical empirical force fields have dominated biomolecular simulations for over 50 years. Although widely used in drug discovery, crystal structure prediction, and biomolecular dynamics, they generally lack the accuracy and transferability required for first-principles predictive modeling. In this paper, we introduce MACE-OFF, a series of short-range transferable force fields for organic molecules created using state-of-the-art machine learning technology and first-principles reference data computed with a high level of quantum mechanical theory. MACE-OFF demonstrates the remarkable capabilities of short-range models by accurately predicting a wide variety of gas- and condensed-phase properties of molecular systems. It produces accurate, easy-to-converge dihedral torsion scans of unseen molecules as well as reliable descriptions of molecular crystals and liquids, including quantum nuclear effects. We further demonstrate the capabilities of MACE-OFF by determining free energy surfaces in explicit solvent as well as the folding dynamics of peptides and nanosecond simulations of a fully solvated protein. These developments enable first-principles simulations of molecular systems for the broader chemistry community at high accuracy and relatively low computational cost.