This dissertation offers a detailed investigation of the use of univariate Hawkes processes to modelconsumer behavior in digital marketing applications. Datapoints in these contexts alternate long periods of sparsity and short bursts of intense activity, presenting many challenges for traditional models. Hawkes processes, meanwhile, provide a flexible framework to capture complex dynamics of dormancy and momentum buildup, but require both adaptation and innovation to appropriately describe consumer data. This dissertation elaborates on their properties, connects them to models in the extant literature, develops new parametric forms, and benchmarks their use in both simulation studies and empirical applications. Special attention is given to empirical estimation under strict privacy laws, a novel and pressing use-case. The model is then extended to the derivation of optimal advertising policies under various market conditions. Ad delivery scheduling, dynamic bidding, and constrained bidding problems are studied analytically, in simulation, and empirically. Once more, special attention is given to the positive and negative impacts of privacy laws for both consumers and advertisers. This work highlights the empirical and theoretical advantages of Hawkes processes as models of dynamic human behavior, as well as both the costs and benefits of emerging privacy policies.