At small length-scales, capillary effects are significant, and thus the mechanics of soft material interfaces may be dominated by solid surface stresses or liquid surface tensions. The balance between surface and bulk properties is described by an elasto-capillary length-scale, in which equilibrium interfacial energies are constant. However, at small length-scales in biological materials, including living cells and tissues, interfacial energies are not constant but are actively regulated and driven far from equilibrium. Thus, the balance between surface and bulk properties depends upon the distance from equilibrium. Here, we model the spreading (wetting) of living cell aggregates as ‘active droplets’, with a non-equilibrium surface tension that depends upon internal stress generated by the actomyosin cytoskeleton. Depending upon the extent of activity, droplet surface properties adapt to the mechanics of their surroundings. The impact of this adaptation challenges contemporary models of interfacial mechanics, including extensively used models of contact mechanics and wetting.