The surface tension of a curved surface behaves differently than that of a planar surface; however, the curvature correction to the surface tension - known as Tolman's length - is commonly ignored in engineering practice. We show that fluid asymmetry, either inherent in binary or ternary systems, or introduced into a pure or binary fluid by the addition of an impurity, can result in an asymmetric concentration profile and diverging Tolman's length at the critical point. The divergence of Tolman's length originates from the critical fluctuations and does not exist in mean-field theories. However, the amplitude of this divergence can be obtained from an appropriate mean-field model. The diverging curvature correction may have a significant impact on the interfacial properties of micro-droplets of such fluids. In a ternary mixture the phase coexistence is generally asymmetric in nature. We model the asymmetric two-phase equilibrium in a ternary mixture using mean-field approximations and the so-called “complete scaling” approach. The resultant asymmetry parameter is used to characterize the curvature correction to the interfacial tension of drops and bubbles in the critical region.