The effect of fluctuations and anisotropy on the transition from the normal to the superconducting state are studied. Neglecting magnetic fluctuations, which is justified as long as the Ginzburg-Landau parameter κ≫1, the critical behavior belongs to the xy-universality class including superfluid helium. Since κ(t)=κ0t2/3, where t=1-T/Tc, upon approaching Tc further, the intrinsic fluctuating magnetic field might change the nature of the transition. Concentrating on the xy-regime, we derive with the aid of the helicity modulus a universal relation between Tc and the amplitudes of the phase correlation length and penetration depth. We also extend the universal critical point amplitude relations to the case of superconductors with uniaxial mass anisotropy. Our analysis of recent specific heat and excess dc conductivity measurement suggest that for both static and dynamic properties three-dimensional critical behavior has been observed. The λ-like specific heat singularity points to critical xy-behavior. Further evidence is provided in terms of the universal amplitude relations, providing estimates for the amplitudes of the correlation lengths for the magnitude and phase of the order parameter and the London penetration depth. We find remarkable agreement with experiment and the correlation volume is comparable to that in superfluid helium. © 1992 Springer-Verlag.