Viruses have established symbiotic relationships with almost every other living organism on Earth and at all levels of biological organisation, from other viruses up to entire ecosystems. In most cases, peacefully coexisting with their hosts, but in most relevant cases, parasitising them and inducing diseases. Viruses are playing an essential role in shaping the eco-evolutionary dynamics of their hosts, and have been also involved in some of the major evolutionary innovations either by working as vectors of genetic information or by being themselves coopted by the host into their genomes. Viruses can be studied at different levels of biological organisation, from the molecular mechanisms of genome replication, gene expression and encapsidation, to global pandemics. All these levels are different and yet connected through the presence of threshold conditions allowing for the formation of a capsid, the loss of genetic information or epidemic spreading. These thresholds, as it occurs with temperatures separating phases in a liquid, define sharp qualitative types of behaviour. These {\em phase transitions} are very well known in Physics. They have been studied by means of simple, but powerful models able to capture their essential properties, allowing to understand them. Can the physics of phase transitions be an inspiration for our understanding of viral dynamics at different scales? Here we review well-known examples of transition phenomena in virology and their simplest mathematical modelling approaches. We suggest that the advantages of abstract, simplified pictures used in Physics are also the key to properly understand the origins and evolution of complexity in viruses. By means of several examples, we explore this multilevel landscape and how minimal models provide deep insights into a diverse array of problems. The relevance of these transitions in connecting dynamical patterns across levels and their evolutionary and clinical implications are outlined.