We review a striking array of recent experiments and their theoretical interpretations on the superfluid transition in 4He in the presence of a heat flux Q . We define and evaluate a new set of critical point exponents. The statics and dynamics of the superfluid-normal interface are discussed, with special attention to the role of gravity. If Q is in the same direction as gravity, a self-organized state can arise, in which the entire sample has a uniform reduced temperature, on either the normal or superfluid side of the transition. Finally, we review recent theory and experiment regarding the heat capacity at constant Q . The excitement that surrounds this field arises from the fact that advanced thermometry and the future availability of a microgravity experimental platform aboard the International Space Station will soon open to experimental exploration decades of reduced temperature that were previously inaccessible.