Viruses have very short and compact genomes and very high mutation rates. Despite these characteristics, they are known to evolve by bursts, periods of high evolution rates alternating with periods of high stability. The mechanisms that drive such switches from slow to fast evolutionary dynamics are mostly unknown although it has often been proposed that bursts of evolution may be triggered by environmental changes or by the occurrence of deleterious events. Here, we simulated the evolution of viral strains using the aevol simulator. By tracking down the long term evolution of 100 virus-like strains derived from 10 different wild-types, we were able to identify 16 strains undergoing bursts of fast evolutionary rates. By analyzing these 16 strains, we were able to identify the events triggering the bursts. At first sight these events were very diverse, some being beneficial while others were (slightly) deleterious, some being large scale chromosomal rearrangements while others were local mutations. However, most of them share a common characteristic: they strongly increase the evolvability of the viral strains, thus opening the door for further favorable mutations to be fixed until this gained evolvability is exhausted and goes back to a very low value, marking the beginning of a new long period of evolutionary stasis.