We present extensive datasets for a class of intermediate-luminosity optical transients known as "luminous red novae" (LRNe). They show doublepeaked light curves, with an initial rapid luminosity rise to a blue peak (at -13 to -15mag), which is followed by a longer-duration red peak that sometimes is attenuated, resembling a plateau. The progenitors of three of them (NGC4490-2011OT1, M101-2015OT1, and SNhunt248), likely relatively massive blue to yellow stars, were also observed in a pre-eruptive stage when their luminosity was slowly increasing. Early spectra obtained during the first peak show a blue continuum with superposed prominent narrow Balmer lines, with P Cygni profiles. Lines of FeII are also clearly observed, mostly in emission. During the second peak, the spectral continuum becomes much redder, H{alpha} is barely detected, and a forest of narrow metal lines is observed in absorption. Very late-time spectra (~6 months after blue peak) show an extremely red spectral continuum, peaking in the infrared (IR) domain. H{alpha} is detected in pure emission at such late phases, along with broad absorption bands due to molecular overtones (such as TiO, VO). We discuss a few alternative scenarios for LRNe. Although major instabilities of single massive stars cannot be definitely ruled out, we favour a common envelope ejection in a close binary system, with possibly a final coalescence of the two stars. The similarity between LRNe and the outburst observed a few months before the explosion of the Type IIn SN 2011ht is also discussed.