We present deep Swift follow-up observations of a sample of 94 unidentified X-ray sources from the XMM–Newton Slew Survey. The X-ray Telescope (XRT) on-board Swift detected 29 per cent of the sample sources; the flux limits for undetected sources suggest the bulk of the Slew Survey sources are drawn from one or more transient populations. We report revised X-ray positions for the XRT-detected sources, with typical uncertainties of 2.9 arcsec, reducing the number of catalogued optical matches to just a single source in most cases. We characterize the sources detected by Swift through their X-ray spectra and variability and via Ultraviolet–Optical Telescope photometry and using catalogued near-infrared, optical and radio observations of potential counterparts. Six sources can be associated with known objects and eight sources may be associated with unidentified ROSAT sources within the 3σ error radii of our revised X-ray positions. We find 10 of the 30 XRT- and/or Burst Alert Telescope (BAT)-detected sources are clearly stellar in nature, including one periodic variable star and two high proper motion stars. For 11 sources we propose an active galactic nucleus (AGN) classification, among which four are detected in hard X-rays and three have redshifts spanning z= 0.2–0.9 obtained from the literature or from optical spectroscopy presented here. A further three sources are suspected AGN and one is a candidate Galactic hard X-ray flash, while five sources remain unclassified. The 67 Slew Survey sources we do not detect with Swift XRT or BAT are studied via their characteristics in the Slew Survey observations and by comparison with the XRT- and BAT-detected population. We suggest that these are mostly if not all extragalactic, though unlikely to be highly absorbed sources in the X-rays such as Compton thick AGN. A large number of these are highly variable soft X-ray (0.2–2 keV) sources and a smaller number are highly variable hard (2–12 keV) sources. A small fraction of mainly hard-band Slew Survey detections may be spurious. This follow-up programme brings us a step further to completing the identifications of a substantial sample of XMM–Newton Slew Survey sources, important for understanding the nature of the transient sky and allowing flux-limited samples to be constructed.