We present a sample of ~1000 emission-line galaxies at z=0.4-4.7 from the ~0.7deg^2^ High-z Emission-Line Survey in the Bootes field identified with a suite of six narrow-band filters at ~=0.4-2.1{mu}m. These galaxies have been selected on their Ly{alpha} (73), [OII] (285), H{beta}/[OIII] (387) or H{alpha} (362) emission line, and have been classified with optical to near-infrared colours. A subsample of 98 sources have reliable redshifts from multiple narrow-band (e.g. [OII]-H{alpha}) detections and/or spectroscopy. In this survey paper, we present the observations, selection and catalogues of emitters. We measure number densities of Ly{alpha}, [OII], H{beta}/[OIII] and H{alpha} and confirm strong luminosity evolution in star-forming galaxies from z~0.4 to ~5, in agreement with previous results. To demonstrate the usefulness of dual-line emitters, we use the sample of dual [OII]-H{alpha} emitters to measure the observed [OII]/H{alpha} ratio at z=1.47. The observed [OII]/H{alpha} ratio increases significantly from 0.40+/-0.01 at z=0.1 to 0.52+/-0.05 at z=1.47, which we attribute to either decreasing dust attenuation with redshift, or due to a bias in the (typically) fibre measurements in the local Universe that only measure the central kpc regions. At the bright end, we find that both the H{alpha} and Ly{alpha} number densities at z~=2.2 deviate significantly from a Schechter form, following a power law. We show that this is driven entirely by an increasing X-ray/active galactic nucleus fraction with line luminosity, which reaches ~=100 per cent at line luminosities L>=3x10^44^erg/s.