The eruption of invasive wild pigs (IWPs) Sus scrofa throughout the world exemplifies the need to understand the influences of exotic and non-native species expansions. In particular, the continental USA is precariously threatened by a rapid expansion of IWPs, and a better understanding of the rate and process of spread can inform strategies that will limit the expansion. We developed a spatially and temporally dynamic model to examine three decades (1982–2012) of IWP expansion, and predict the spread of IWPs throughout the continental USA, relative to where IWPs previously inhabited. We used the model to predict where IWPs are likely to invade next. The average rate of northward expansion increased from 6.5 to 12.6 km per year, suggesting most counties in the continental USA could be inhabited within the next 3–5 decades. The spread of IWPs was primarily associated with expansion into areas with similar environmental characteristics as their previous range, with the exception of spreading into colder regions. We identified that climate change may assist spread into northern regions by generating milder winters with less snow. Otherwise, the spread of IWPs was not dependent on agriculture, precipitation, or biodiversity at the county level. The model correctly predicted 86% of counties that were invaded during 2012, and those predictions indicate that large portions of the USA are in immediate danger of invasion. Synthesis and applications. Anti-invasion efforts should focus along the boundaries of current occupied range to stop natural expansion, and anti-invasion policies should focus on stopping anthropogenic transport and release of invasive wild pigs (IWPs). Our results demonstrate the utility of a spatio-temporal examination to inform strategies for limiting the spread of IWPs.