Abstract We present Lyα and ultraviolet (UV)-continuum luminosity functions (LFs) of galaxies and active galactic nuclei (AGNs) at z = 2.0–3.5 determined by the untargeted optical spectroscopic survey of the Hobby–Eberly Telescope Dark Energy Experiment (HETDEX). We combine deep Subaru imaging with HETDEX spectra resulting in 11.4 deg² of fiber spectra sky coverage, obtaining 18,320 galaxies spectroscopically identified with Lyα emission, 2126 of which host type 1 AGNs showing broad (FWHM > 1000 km s⁻¹) Lyα emission lines. We derive the Lyα (UV) LF over 2 orders of magnitude covering bright galaxies and AGNs in log L Ly α / [ erg s − 1 ] = 43.3 – 45.5 (−27 < M _UV < −20) by the 1/V _max estimator. Our results reveal that the bright-end hump of the Lyα LF is composed of type 1 AGNs. In conjunction with previous spectroscopic results at the faint end, we measure a slope of the best-fit Schechter function to be α Sch = − 1.70 − 0.14 + 0.13 , which indicates that α _Sch steepens from z = 2–3 toward high redshift. Our UV LF agrees well with previous AGN UV LFs and extends to faint-AGN and bright-galaxy regimes. The number fraction of Lyα-emitting objects (X _LAE) increases from M UV * ∼ − 21 to bright magnitude due to the contribution of type 1 AGNs, while previous studies claim that X _Lyα decreases from faint magnitudes to M UV * , suggesting a valley in the X _Lyα –magnitude relation at M UV * . Comparing our UV LF of type 1 AGNs at z = 2–3 with those at z = 0, we find that the number density of faint (M _UV > −21) type 1 AGNs increases from z ∼ 2 to 0, as opposed to the evolution of bright (M _UV < −21) type 1 AGNs, suggesting AGN downsizing in the rest-frame UV luminosity.