The effect of line tension may increase or decrease the potential barrier separating the Cassie and the Wenzel wetting states, depending on the sign of the line tension and the topography of a relief. The formation of the barrier separating the Cassie and Wenzel wetting states on reentrant topographies, which demonstrate pronounced superhydrophobicity and superoleophobicity, is treated. Various topographies giving rise to high apparent contact angles are discussed. It spite of the fact that the line tension is regarded as a weak effect, it may be essential for stabilizing (destabilizing) the Cassie wetting. The effect may be crucial to understanding the stability of the Cassie-like wetting of inherently hydrophilic nanoscaled reliefs.