The orbital evolution and final fate of interacting binaries are strongly influenced by mass transfer (MT). Classical binary-evolution theory generally assumes circular orbits during MT, yet nonzero eccentricities are commonly observed in wide post-interaction binaries, and their origin remains unclear. Eccentric MT offers a promising solution.

In this work, we confront the general mass-transfer (GeMT) model, the first complete framework for MT at arbitrary eccentricity, with observations of wide sdB+MS binaries. We isolate the effects of eccentric MT and show that it naturally reproduces their observed orbital-parameter distributions and correlations. We further demonstrate that generally post-MT eccentricity depends directly on key MT properties, including transferred mass, accretion efficiency, and angular-momentum loss. Given the multitude of eccentric post-MT binaries with components ranging from low- to high-mass stars to compact objects, we propose that post-MT eccentricities offer a new window onto binary evolution, presenting a powerful tool to constrain highly uncertain binary-evolution parameters and mass-transfer formation histories across diverse populations. Post-MT eccentricity should therefore be embraced as a key observable, rather than treated as a problem to be corrected.

Binary star systems are common: at least half of solar-type stars and nearly all massive stars reside in binaries. Binary interactions such as mass transfer, tides, common-envelope phases, and mergers profoundly alter stellar evolution, producing various phenomena that single-star evolution cannot explain. Examples range from chemically peculiar stars and blue stragglers to supernovae, gamma-ray bursts, and gravitational-wave mergers. More recently, large surveys, such as Gaia and TESS, have revolutionized our census of binaries across the Galaxy, revealing that eccentricity in wide, evolved post-interaction systems is far more common than previously thought. This suggests a fundamental link between binary interactions and orbital eccentricity, yet the theoretical origin remains poorly understood and synthetic models still struggle to reproduce the observed orbital properties.

In this colloquium, I discuss our evolving understanding of eccentricity in the context of interacting binaries, review different eccentricity-pumping mechanisms and present the General Mass Transfer (GeMT) model, a new semianalytic framework for the secular orbital evolution of mass-transferring (MT) binaries. By comparing predictions to observations, I demonstrate that nonzero eccentricity is a natural outcome of MT and depends directly on key MT parameters. Given the multitude of eccentric post-MT binaries with components ranging from low- to high-mass stars to compact objects, I show that post-MT eccentricities offer a new window onto binary evolution, presenting a powerful tool to constrain uncertain MT parameters and formation histories across diverse populations