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Renormalization is a conceptual framework and set of technical procedures in quantum field theory and statistical physics for dealing with infinities that arise in calculations and for understanding how physical quantities depend on energy or length scales. In perturbative quantum field theory, loop integrals produce ultraviolet divergences. Regularization introduces a regulator, such as a momentum cutoff or dimensional regularization, to control these divergences. Renormalization then absorbs the regulator-dependent parts into redefined parameters like masses and coupling constants, yielding finite predictions for observable quantities. The dependence of these parameters on the renormalization scale is governed by renormalization group equations, which describe how effective theories change with energy scale.

The key distinction is between renormalizable theories, which require only a finite set of counterterms to absorb divergences, and nonrenormalizable theories, which in principle need infinitely many counterterms but can be meaningful as effective field theories valid up to a cutoff. The renormalization group also explains universality near critical points in statistical systems: details at microscopic scales become irrelevant, and large-scale behavior is governed by fixed points and relevant operators.

Historically, the concept developed through Bogoliubov and Shirkov, Zimmermann, and later Kenneth Wilson, who formulated the modern Wilsonian renormalization group. In particle physics, renormalization underpins the success of the Standard Model, with running couplings measured at different energies. In summary, renormalization provides a consistent way to remove unphysical dependencies and to understand how theories behave across scales, linking high-energy physics, critical phenomena, and effective field theories.