In physics, the adjective renormalizable refers to a theory (usually a quantum field theory) in which all ultraviolet divergences, infinities and other seemingly meaningless results can be cured by the process of renormalization. This means that the number of "independent types" of ultraviolet infinities must be finite, and by setting them equal to the measured values, we can predict the results of all other experiments.
Quantum chromodynamics (QCD) is a very good example of a renormalizable theory, due to the asymptotic freedom. Quantum electrodynamics (QED) is perturbatively renormalizable, but non-perturbatively ill-defined because of the existence of Landau pole.
On the other hand, Fermi's interaction or general relativity are non-renormalizable. This problem is a hint that these theories should be replaced by a more complete theory at very short distance. These more complete theories are the electroweak theory and string theory, respectively.
