This dissertation investigates typological patterns of syntax and morphosyntax, and the role that learning biases play in constraining them. A link between learning biases and typology is integral to generative linguistics, however evidence for this connection remains minimal. Using experimental, theoretical, and mathematical tools, I provide support for two types of biases: substantive biases (dis)favoring particular structures, and a formal regularization bias favoring the minimization of variation. I develop the Mixture Shift Paradigm, an artificial language learning paradigm based on Hudson Kam & Newport (2005), motivated by the idea that typological patterns result from gradual changes affected by learners. The paradigm introduces learners to variable input, and observes the extent to which they alter the language to bring it in line with hypothesized biases. In Chapter 2, I use this paradigm to show that learners exposed to noun, adjective, and numeral ordering patterns exhibit regularization constrained by a substantive bias in line with cross-linguistic typology (Greenberg 1963). Chapter 3 develops a Bayesian model of the acquisition of these ordering patterns. In Chapter 4, I investigate the effect of feedback on learners, and discuss broader issues concerning the nature of learning biases, and whether they are specific to language or domain-general. In Chapters 5 and 6, I turn to a recurrent pathway of change involving grammaticalization of pronominal elements into agreement markers. I provide evidence of this process in Colloquial French, showing that the development of a new system of agreement from subject clitics fits into a wider cross-linguistic typology of change. I then present the results of an experiment, using the Mixture Shift Paradigm, showing that learners regularize patterns of agreement, but only when they are in line with cross-linguistically attested patterns. This experiment offers further evidence that learning biases (both formal and substantive) constrain linguistic change, resulting in recurrent typological patterns that provide insight into the nature of the language acquisition mechanism.