The extremely close proximity of hot Jupiters to their parent stars has dramatically affected both their atmospheres and interiors, inflating them to up to twice the radius of Jupiter. The physical mechanism responsible for this inflation remains unknown, though many proposals have been put forward. I will review the known hot Jupiter population, the proposed inflation mechanisms, and the evidence for and against them collected thus far. In doing so, I will cover the ways that hot Jupiter interiors may be simulated computationally in detail, and present some useful formulas for estimating their radii, heating, intrinsic temperature, and tentative magnetic field strength. I will also cover the related issues of hot Jupiter intrinsic temperatures and radiative-convective boundaries, the potential connection with planetary magnetic fields, and the effects of stellar tides on the planet. Finally, I conclude with the suggestion that more than one mechanism may be operating in concert with each other and propose various avenues for future progress in understanding these objects.
Comment: To be published in: Handbook of Exoplanets, 2nd Edition, Hans Deeg and Juan Antonio Belmonte (Eds. in Chief), Springer International Publishing AG, part of Springer Nature. This revision implements minor fixes to resolve missing words and an incorrect citation