We explore the origin of the observed Lyα and other ultraviolet (UV) lines from galaxies at z < 3.7 by detailed modelling of their spectra. The objects are chosen from among those showing (a) UV–optical–near-IR lines, (b) only UV lines and (c) Lyα in the UV and a few optical lines. The total sample is heterogeneous, including galaxies in an all-sky radio survey, hard X-ray-emitting sources, a type 2 quasar (QSR)identified as a X-ray source, a type 2 active galactic nucleus (AGN) at high z (3.7), a very extended Lyα-emitting nebula, objects in a multi-band imaging survey for Lyman-break galaxies and in a slitless spectroscopic survey for Lyman-alpha emitters (LAEs), etc. We also present UV line predictions for a sample of galaxies in the 0.0686 < z < 0.8829 range. For calculation of the line and continuum spectra, we use the code suma, which accounts consistently for photoionizing flux from an external source and shocks. Dust-reprocessed radiation is also calculated. The results show that calculated Lyα/Hβ values are generally higher than observed, except for a few starburst (SB)-dominated models. Some spectra are better reproduced by shock-dominated models. The sample of galaxies including the Lyα line shows neither peculiar gas physical conditions nor abnormal element abundances. The line profiles have complex full widths at half maximum (FWHM) with two main components, which translate into two types of emitting gas clouds. High T * values (>105 K), which indicate that SB stars are close to outburst, were found in a few objects. Traces of supernova events are suggested by a scandium emission line from the SST24 nebula and by shock-dominated models.