ABSTRACT Cosmological observations usually map our present-day past light cone. However, it is also possible to compare different past light cones. This is the concept behind the redshift drift, a model-independent probe of fundamental cosmology. In simple physical terms, this effectively allows us to watch the Universe expand in real time. While current facilities only allow sensitivities several orders of magnitude worse than the expected signal, it should be possible to detect it with forthcoming ones. Here, we discuss the potential impact of measurements by three such facilities: the Extremely Large Telescope (the subject of most existing redshift drift forecasts), but also the Square Kilometre Array and intensity mapping experiments. For each of these we assume the measurement sensitivities estimated respectively in Liske et al. (2008), Klockner et al. (2015), and Yu, Zhang & Pen (2014). We focus on the role of these measurements in constraining dark energy scenarios, highlighting the fact that although on their own they yield comparatively weak constraints, they do probe regions of parameter space that are typically different from those probed by other experiments, as well as being redshift dependent. Specifically, we quantify how combinations of several redshift drift measurements at different redshifts, or combinations of redshift drift measurements with those from other canonical cosmological probes, can constrain some representative dark energy models. Our conclusion is that a model-independent mapping of the expansion of the universe from redshift z = 0 to z = 4 – a challenging but feasible goal for the next generation of astrophysical facilities – can have a significant impact on fundamental cosmology.