Bacteriophages, phages for short, are viruses of bacteria. The majority of phages contain a double-stranded DNA genome packaged in a capsid at a density of ∼ 500 mg/ml. This high density requires substantial compression of the normal B form helix, leading to the conjecture that DNA in mature phage virions is under significant pressure, and that pressure is used to eject the DNA during infection. A large number of theoretical, computer simulation and in vitro experimental studies surrounding this conjecture has revealed many -though often isolated and/or contradictory -aspects of packaged DNA. This prompts us to present a unified view of the statistical physics and thermodynamics of DNA packaged in phage capsids. We argue that the DNA in a mature phage is in a (meta)stable state, wherein electrostatic self-repulsion is balanced by curvature stress due to confinement in the capsid. We show that in addition to the osmotic pressure associated with the packaged DNA and its counterions, there are four different pressures within the capsid: pressure on the DNA, hydrostatic pressure, the pressure experienced by the capsid, and the pressure associated with the chemical potential of DNA ejection. Significantly, we analyze the mechanism of force transmission in the packaged DNA, and demonstrate that the pressure on DNA is not important for ejection. We derive equations showing a strong hydrostatic pressure difference across the capsid shell. We propose that when a phage is triggered to eject by interaction with its receptor in vitro, the (thermodynamic) incentive of water molecules to enter the phage capsid flushes the DNA out of the capsid. In vivo, the difference between the osmotic pressures in the bacterial cell cytoplasm and the culture medium similarly results in a water flow that drags the DNA out of the capsid and into the bacterial cell.