Abstract: Cluster algebras are characterized by binomial exchange relations. A natural generalization of these algebras, introduced by Chekhov and Shapiro, relaxes this restriction and allows the exchange polynomials to have arbitrarily many terms. Following the work of Gross, Hacking, Keel, and Kontsevich, we give a construction of generalized cluster scattering diagrams, generalized cluster varieties, and theta bases for reciprocal generalized cluster algebras. This is joint work with Man-Wai Cheung and Gregg Musiker.