Contact binaries challenge contemporary stellar astrophysics with respect to their incidence, structure, and evolution. We explore these issues through a detailed study of two bright examples: S Ant and $\varepsilon$ CrA, that permit high-resolution spectroscopy at a relatively good S/N ratio. The availability of high-quality photometry, including data from the TESS satellite as well as Gaia parallaxes, allows us to apply the Russell paradigm to produce reliable up-to-date information on the physical properties of these binaries. As a result, models of their interactive evolution, such as the thermal relaxation oscillator scenario, can be examined. Mass transfer between the components is clearly evidenced, but the variability of the O’Connell effect over relatively short-time scales points to irregularities in the mass transfer or accretion processes. Our findings indicate that S Ant may evolve into an R CMa type Algol, while the low mass ratio of $\varepsilon$ CrA suggests a likely merger of its components in the not-too-distant future.