Deep narrow-band surveys have revealed a large population of faint Ly{alpha} emitters (LAEs) in the distant Universe, but relatively little is known about the most luminous sources (L_Lya_>~10^42.7^erg/s; L_Lya>~L^*^_Lya_). Here we present the spectroscopic follow-up of 21 luminous LAEs at z~2-3 found with panoramic narrow-band surveys over five independent extragalactic fields (=~4x10^6^Mpc^3^ surveyed at z~2.2 and z~3.1). We use WHT/ISIS, Keck/DEIMOS, and VLT/X-SHOOTER to study these sources using high ionization UV lines. Luminous LAEs at z~2-3 have blue UV slopes ({beta}=-2.0^+0.3^_-0.1_) and high Ly{alpha} escape fractions (50^+20^_-15_ per cent) and span five orders of magnitude in UV luminosity (M_UV_=~-19 to -24). Many (70 per cent) show at least one high ionization rest-frame UV line such as CIV, NV, CIII], HeII or OIII], typically blue-shifted by =~100-200km/s relative to Ly{alpha}. Their Ly{alpha} profiles reveal a wide variety of shapes, including significant blue-shifted components and widths from 200 to 4000km/s. Overall, 60+/-11 per cent appear to be active galactic nucleus (AGN) dominated, and at L_Lya_>10^43.3^erg/s and/or M_UV_<-21.5 virtually all LAEs are AGNs with high ionization parameters (logU=0.6+/-0.5) and with metallicities of =~0.5-1Z_{sun}_. Those lacking signatures of AGNs (40+/-11 per cent) have lower ionization parameters (logU=-3.0^+1.6^_-0.9_ and log{xi}_ion_=25.4+/-0.2) and are apparently metal-poor sources likely powered by young, dust-poor 'maximal' starbursts. Our results show that luminous LAEs at z~2-3 are a diverse population and that 2xL^*^_Lya_ and 2*M_UV_^*^ mark a sharp transition in the nature of LAEs, from star formation dominated to AGN dominated.