Quality improvement methods are essential to gathering high-quality crowdsourced data, both for research and industry applications. A popular and broadly applicable method is task assignment that dynamically adjusts crowd workflow parameters. In this survey, we review task assignment methods that address: heterogeneous task assignment, question assignment, and plurality problems in crowdsourcing. We discuss and contrast how these methods estimate worker performance, and highlight potential challenges in their implementation. Finally, we discuss future research directions for task assignment methods, and how crowdsourcing platforms and other stakeholders can benefit from them.