Deep narrow-band surveys have revealed a large population of faint Lyman-alpha (Lya) emitters (LAEs) in the distant Universe, but relatively little is known about the most luminous sources. I will present the results of the follow-up of a large sample of luminous LAEs at z~2-3 found with panoramic narrow-band surveys over five independent extragalactic fields (~4x10^6 Mpc^3 surveyed). We use WHT/ISIS, Keck/DEIMOS and VLT/X-SHOOTER to study these sources using high ionisation rest-frame UV lines. Luminous LAEs at z~2-3 have blue UV slopes, high Lya escape fractions and span five orders of magnitude in UV luminosity, covering the parameter space occupied by galaxies, faint and more typical AGN. Many (70%) show at least one high ionisation rest-frame UV line such as CIV, NV, CIII], HeII or OIII], typically blue-shifted by ~100-200 km/s relative to Lya. Overall, 60+-11% appear to be AGN dominated, and at L>10^43.3 erg/s and/or MUV−21.5 virtually all LAEs are AGN with high ionisation parameters and close to solar metallicities. Those lacking signatures of AGN (40+-11%) have lower ionisation parameters and are apparently metal-poor sources likely powered by young, dust-poor "maximal" starbursts. Our results show that luminous LAEs are a diverse population and that 2L∗ and 2xM∗ mark an extremely sharp transition in the nature of LAEs, from star formation dominated to AGN dominated.