The EBLM Project -- From False Positives to Benchmark Stars and Circumbinary Exoplanets

The EBLM project aims to characterise very low-mass stars that are companions to solar-type stars in eclipsing binaries. We describe the history and motivation for this project, the methodology we use to obtain precise mass, radius and effective temperature estimates for very low-mass M-dwarfs, and review results of the EBLM study and those from related projects. We show that radius inflation in fully-convective stars is a more subtle effect than was previously thought based on less precise measurements, i.e. the mass-radius-effective temperature relations we observe for fully-convective stars in single-line eclipsing binaries show reasonable agreement with theoretical models, particularly if we account for the M-dwarf metallicity, as inferred from the analysis of the primary star spectrum.