We review and analyze experiment results of the specific heat, the muon-spin rotation (muSR) relaxation rate and the fluctuation contributions to the magnetization and dc conductivity of extreme type II superconductors from the point of view of critical phenomena. Our estimates of critical exponents and amplitudes, the measured scaling behavior, the consistencies with the universal relations between the critical amplitudes and the decrease of the transition temperature (T(c)) with decreasing thickness, which corresponds to a dimensional crossover from 3d and 2d xy critical behavior, provide considerable evidence for a three-dimensional xy critical point. The estimated volume of the critical correlation length amplitudes turns out to be comparable to that in super-fluid Helium and is several orders of magnitude smaller than in BCS superconductors. Moreover, motivated by the Uemura plot, which relates the measured T(c) to the zero temperature muSR relaxation rate, and by the hyperuniversal relation between T(c) and critical amplitudes of the London penetration depth and phase correlation length, we propose a simple 'universal' scaling ansatz, where the plot of the rescaled transition temperature versus rescaled muSR relaxation rate should fall on a single parabola. Our analysis of the muSR data reveals excellent agreement with this scaling ansatz for a large class of cuprate and Chevrel-phase superconductors. The resulting dependence of T(c) on the zero-temperature ''condensate density'' is then used to explore universal trends in the pressure (alpha) and isotope (beta) coefficients. In good agreement with experiment we find that alpha and beta fall into common T(c)-alpha and T(c)-beta regions, respectively, forming two branches, one for systems with positive and the other for compounds with negative pressure or isotope coefficient. The two brandies merge at the maximum T(c) where the coefficients vanish and the magnitude of the coefficients increases with decreasing T(c). The ''universal'' scaling ansatz also implies that the critical amplitudes of the penetration depth and phase correlation length are related to the zero temperature condensate density. This quantity is also related to the hole concentration. Finally we discuss the temperature dependence of the penetration depth. MuSR measurements indicate that for various cuprates the temperature dependence for 0 < T < T(c) appears to be bounded by the two-fluid model and the dilute charged Bose gas behaviors, respectively. Consistent with the dependence of T(c) on the zero temperature condensate density, compounds with high T(c)'s turn out to be doser to two-fluid behavior, while compounds with decreasing T(c) and in turn with lower condensate density clearly reveal the crossover to the dilute gas limit. These trends combined with T --> 0 point uniquely to Bose condensation of interacting and weakly charged pairs as the mechanism that drives the transition.
