To survive, many biological organisms need to accurately infer which features of their environment predict future rewards and punishments. In machine learning terms, this is the problem of spatial credit assignment, for which many supervised learning algorithms have been developed. In this thesis, I mainly propose that a dual-pathway, regression-like strategy and associated biological implementations may be used to solve this problem. Using David Marr's (1982) three-level philosophy of computational neuroscience, the thesis and its contributions are organized as follows: - Computational Level: Here, the spatial credit assignment problem is formally defined and modeled using probability density functions. The specific challenges of the problem faced by organisms and machine learning algorithms alike are also identified. - Algorithmic Level: I present and evaluate the novel hypothesis that the general strategy used by animals is to perform a regression over past experiences. I also introduce an extension of a probabilistic model for regression that substantially improves generalization without resorting to regularization. This approach subdues residual associations to irrelevant features, as does regularization. - Physical Level: Here, the neuroscience of classical conditioning and of the basal ganglia is briefly reviewed. Then, two novel models of the basal ganglia are put forward: 1) an online-learning model that supports the regression hypothesis and 2) a biological implementation of the probabilistic model previously introduced. Finally, we compare these models to others in the literature. In short, this thesis establishes a theoretical framework for studying the spatial credit assignment problem, offers a simple hypothesis for how biological systems solve it, and implements basal ganglia-based algorithms in support. The thesis brings to light novel approaches for machine learning and several explanations for biological structures and classical conditioning phenomena. / Note: While the thesis contains content from two articles (one journal, one conference), their publishers do not require special permission for their use in dissertations (information confirming this is in an appendix of the thesis itself).