 What follows is a rough overview of perturbative QFT (see James Fraser 2016 for more details). Since exactly solvable free QFT models are more mathematically tractable than interacting QFT models, perturbative QFT treats interactions as perturbations to the free Lagrangian assuming weak coupling. For strongly coupled theories like quantum chromodynamics that idealization fails. Using perturbation theory, approximate solutions for interacting QFT models can be calculated by expanding S-matrix elements in a power series in terms of a coupling parameter. However, the higher order terms will often contain divergent integrals. Typically, renormalization of the higher order terms is required to get finite predictions. Two sources of divergent integrals are infrared (long distance, low energy) and ultraviolet (short distance, high energy) divergences. Infrared divergences are often handled by imposing a long distance cutoff or putting a small non-zero lower limit for the integral over momentum. A sharp cutoff at low momentum is equivalent to putting the theory in a finite volume box. Imposing asymptotic boundary conditions and restricting the observables to long distance “friendly” observables also help with infrared divergences. Ultraviolet divergences are often handled by imposing a momentum cutoff to remove high momentum modes of a theory. That is equivalent to freezing out variations in the fields at arbitrarily short length scales. Putting the system on a lattice with some finite spacing can also help deal with the high momentum. Dimensional regularization, where the integral measure is redefined to range over a fractional number of dimensions, can help with both infrared and ultraviolet divergences. The last step in renormalization is to remove the cutoffs by taking the continuum limit (i.e., removing the high momentum cutoff) and the infinite volume limit (i.e., removing the low momentum cutoff). The hope is that the limit is well-defined and there are finite expressions of the series at each order.