Justifying Dimensional Regularization

In the computation of Feynman integrals divergences are common. To make sense of the divergent integral we employ a regulator so we can manipulate a well defined object. Many regulators are available and have various pros and cons. One of the most common choices is dimensional regularization where we analytically continue our integral to an arbitrary complex dimension where we can evaluate the integral and extract the divergence. This works wonderfully but what does integration in 3.9999 dimensions mean? How well is this defined? Is it just a set of rules to follow and hope for the best? In this talk I hope to justify that this is well defined and show that dimensional integration has all the properties we need to calculate Feynman integrals. This will not be a perfect proof and will largely follow the one presented in Collins Renormalization.