We consider a problem of interference between two independent condensates, which lack true long range order. We show that their interference pattern contains information about correlation functions within each condensate. As an example we analyze the interference between a pair of one dimensional interacting Bose liquids. We find universal scaling of the average fringe contrast with system size and temperature that depends only on the Luttinger parameter. Moreover the full distribution of the fringe contrast, which is also equivalent to the full counting statistics of the interfering atoms, changes with interaction strength and lends information on high order correlation functions. We also demonstrate that the interference between two-dimensional condensates at finite temperature can be used as a direct probe of the Kosterlitz-Thouless transition. Finally, we discuss generalization of our results to describe the intereference of a periodic array of independent fluctuating condensates.