Hidden Patterns in the Standard Model

One famous physics popularizer has claimed that while the Standard Model is "the most successful physical theory ever proposed, it is also one of the ugliest". Another possibility is that the Standard Model is more beautiful than we realize, and holds clues we do not yet understand. Here we review some attempts to find hidden patterns in the Standard Model, going back to the work of Georgi, Glashow, Pati and Salam but leading up to recent ideas connected to the octonions.