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Half of the energy ever emitted by stars and accreting objects comes to us in the far-infrared (FIR) waveband and has yet to be properly explored. We propose a powerful Far-InfraRed Interferometer mission, FIRI, to carry out high-resolution imaging spectroscopy in the FIR. This key observational capability is essential to reveal how gas and dust evolve into stars and planets, how the first luminous objects in the Universe ignited, how galaxies formed, and when super-massive black holes grew. FIRI will disentangle the cosmic histories of star formation and accretion onto black holes and will trace the assembly and evolution of quiescent galaxies like our Milky Way. Perhaps most importantly, FIRI will observe all stages of planetary system formation and recognise the birth of planets via its ability to image the dust structures in planetary systems. FIRI is an observatory-class mission concept: three cold, 3.5-m apertures, orbiting a beam-combining module, with separations of up to 1 km, free-flying or tethered, operating between 25 and 385 μm, using the interferometric direct-detection technique to ensure μJy sensitivity and 0.02” resolution at 100 μm, across an arcmin2 instantaneous field of view, with a spectral resolution, R ~ 5,000 and a heterodyne system with R ~ 1 million. Although FIRI is an ambitious mission, we note that FIR interferometry is appreciably less demanding than at shorter wavelengths. [ABSTRACT FROM AUTHOR]