The recent pandemic has led to a particular interest in mathematical and computational virology. I have previously given an introduction to virus structure and assembly, in particular the group theory aspect of structure and the modelling aspects of packaging signal-mediated assembly. Here I will focus on three more recent developments in these two areas. Firstly, based on the mechanistic understanding of the viral assembly instruction manual, we have recently proposed a new type of antiviral agent, a Therapeutic Interfering Particle, that parasitises the virus itself and misdirects its assembly. This could open up a whole new approach to antiviral therapy and immunisation. The second example is the demonstration of the usefulness of data science techniques in this field, complementary to the modelling simulations, that allow the machine learning of structure in the data from simulations and experiments. Thirdly, the recent discovery of giant viruses leads to renewed interest in geometric models of virus structure, with potentially predictive power via a scaling relation and quantised geometric blueprints.