This paper presents and discusses a critical compilation of accurate, fundamental determinations of stellar masses and radii. We have identified 95 detached binary systems containing 190 stars (94 eclipsing systems, and α Centauri) that satisfy our criterion that the mass and radius of both stars be known to ±3% or better. All are non-interacting systems, so the stars should have evolved as if they were single. This sample more than doubles that of the earlier similar review by Andersen (1991), extends the mass range at both ends and, for the first time, includes an extragalactic binary. In every case, we have examined the original data and recomputed the stellar parameters with a consistent set of assumptions and physical constants. To these we add interstellar reddening, effective temperature, metal abundance, rotational velocity and apsidal motion determinations when available, and we compute a number of other physical parameters, notably luminosity and distance.These accurate physical parameters reveal the effects of stellar evolution with unprecedented clarity, and we discuss the use of the data in observational tests of stellar evolution models in some detail. Earlier findings of significant structural differences between moderately fast-rotating, mildly active stars and single stars, ascribed to the presence of strong magnetic and spot activity, are confirmed beyond doubt. We also show how the best data can be used to test prescriptions for the subtle interplay between convection, diffusion, and other non-classical effects in stellar models. The amount and quality of the data also allow us to analyse the tidal evolution of the systems in considerable depth, testing prescriptions of rotational synchronisation and orbital circularisation in greater detail than possible before. We show that the formulae for pseudo-synchronisation of stars in eccentric orbits predict the observed rotations quite well, except for very young and/or widely-separated stars. Deviations do occur, however, especially for stars with convective envelopes. The superior data set finally demonstrates that apsidal motion rates as predicted from General Relativity plus tidal theory are in good agreement with the best observational data. No reliable binary data exist that challenge General Relativity to any significant extent.The new data also enable us to derive empirical calibrations of M and R for single (post-) main-sequence stars above 0.6 M ⊙ . Simple, polynomial functions of T eff , log g and [Fe/H] yield M and R with errors of 6% and 3%, respectively. Excellent agreement is found with independent determinations for host stars of transiting extrasolar planets, and good agreement with determinations of M and R from stellar models as constrained by trigonometric parallaxes and spectroscopic values of T eff and [Fe/H].Finally, we list a set of 23 interferometric binaries with masses known to better than 3%, but without fundamental radius determinations (except α Aur). We discuss the prospects for improving these and other stell...
