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. This chapter reviews the known hot Jupiter population, the proposed inflation mechanisms, and the evidence for and against them collected thus far. In doing so, it covers the ways that hot Jupiter interiors may be simulated computationally in detail and presents some useful formulas for estimating their radii, heating, intrinsic temperature, and tentative magnetic field strength. It also covers 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, it concludes with the suggestion that more than one mechanism may be operating in concert with each other and proposes various avenues for future progress in understanding these objects.