While the exact origin and date of start of circulation of SARS-CoV-2 is as yet uncertain, it appears that the disease it causes, COVID-19, started its international spread after an amplification stage that happened in Wuhan (China) in late 2019. Roughly six months later, COVID-19 has been reported in most countries and territories worldwide. In this talk, I will present various models I have studied that aim to understand and sometimes predict this spatial spread. The work revolves around a slight complexification of an SLIAR model that Brauer, van den Driessche, Watmough, Wu and myself had studied in preparation for the last pandemic (H1N1). I will first present this base model and briefly detail its properties. I will then show how the model is being used in three different contexts: a) determination of places most likely to next import the disease, b) assessment of the risk of importation of the disease to an uninfected location and c) evaluation of heterogeneity of transmission characteristics in different locations.