Understanding the molecular mechanisms and biological consequences of genetic changes occurring during bypass of cellular senescence spans a broad area of medical research from the cancer field to regenerative medicine. Senescence escape and immortalisation have been intensively studied in murine embryonic fibroblasts as a model system, and are known to occur when the p53/ARF tumour suppressor pathway is disrupted. We showed recently that murine fibroblasts with a humanised p53 gene (Hupki cells, from a human p53 knock-in mouse model) first senesce, and then become immortalised in the same way as their homologues with normal murine p53. In both cell types, immortalised cultures frequently sustain either a p53 gene mutation matching a human tumour mutation and resulting in loss of p53 transcriptional transactivation, or a biallelic deletion at the p19/ARF locus. Whilst these genetic events were not unexpected, we were surprised to find that a significant proportion of immortalised cell cultures apparently had neither a p53 mutation nor loss of p19/ARF. Here we consider various routes to p53/ARF disruption in senescence bypass, and dysfunction of other tumour suppressor networks that may contribute to release from tenacious cell cycle arrest in senescent cultures.