Biological invasions are one of the most significant threats to marine biodiversity, and can be facilitated and amplified by climate change. Among all aspects of invasion biology, biotic interactions between invaders and native species are of particular importance. They strongly influence the invasion velocity as well as species responses to climate-induced stressors. Yet the effects of biotic interactions and other important demographic processes remain overlooked among most studies of climate-mediated invasions. We critically assessed current modelling techniques for forecasting marine invasions under climate change, with a particular focus on their ability to account for important biotic interactions and demographic processes. We show that coupled range dynamics models currently represent the most comprehensive and promising approach for modelling and managing marine invasions under climate change. We show, using the crown-of-thorns seastar (Acanthaster planci), why model architectures that account for biotic interactions and demographic and spatial processes (and their interaction) are required to provide ecologically realistic predictions of the distribution and abundance of invader species, both under present-day conditions and into the future. We suggest potential solutions to inform data-poor situations, such as Bayesian parameter estimation and meta-analysis, and identify strategic and targeted gaps in marine invasion research.