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There is now a considerable literature on computer simulations of DNA packaging inside bacteriophage capsids. While most studies have reached a semiquantitative or qualitative agreement with single molecule packaging and ejection studies, several quantitative answers are to date still lacking, needing either more accurate measurements or more realistic or difficult simulations. Here, I briefly review the outstanding questions in this field and report some new numerical results on DNA packaging inside the phi29 phage, modelled either as a capped sphero-cylinder or as a sphere with the same internal volume. These simulations include electrostatics and a realistic genome length, and contribute to seriously questioning the inverse spool model, which arises from a purely continuum mechanics view of the problem, and is still commonly adopted to describe the shape of the packaged genome.