Many postsecondary institutions, and community colleges in particular, require that students demonstrate specified levels of literacy and numeracy before taking college-level courses. Typically, students have been assessed using two widely available tests--ACCUPLACER and Compass. However, placement testing practice is beginning to change for three reasons. First, the Compass test will no longer be offered as of the end of 2016. Second, questions have been raised about the validity of commonly used placement tests. Third, there are emerging discussions about the need to consider other aspects of students' readiness to succeed in college, especially so-called noncognitive skills. In this paper, we discuss the history of college placement testing, with a focus on nonselective colleges. We describe the limitations of placement tests, the consequences of placement errors, and the movement toward changing systems of placement. The use of multiple measures is suggested as an approach that will result in more accurate placement. A typology of approaches to assessment and placement is described, including the identification of individual measures (e.g., alternative math and English tests, noncognitive assessments, and high school transcript information), ways to use them in combination (e.g., waivers, decision rules, and placement formulae), and how colleges might use assessment results in more varied ways (e.g., for placement into different course types or services). Finally, we include a discussion of emerging issues affecting assessment and placement practices.