Empirical studies and evolutionary theory support a role for rare variants in the etiology of complex traits. Given this motivation and increasing affordability of whole-exome and whole-genome sequencing, methods for rare variant association have been an active area of research for the past decade. Here, we provide a survey of the current literature and developments from the Genetics Analysis Workshop 19 (GAW19) Collapsing Rare Variants working group. In particular, we present the generalized linear regression framework and associated score statistic for the 2 major types of methods: burden and variance components methods. We further show that by simply modifying weights within these frameworks we arrive at many of the popular existing methods, for example, the cohort allelic sums test and sequence kernel association test. Meta-analysis techniques are also described. Next, we describe the 6 contributions from the GAW19 Collapsing Rare Variants working group. These included development of new methods, such as a retrospective likelihood for family data, a method using genomic structure to compare cases and controls, a haplotype-based meta-analysis, and a permutation-based method for combining different statistical tests. In addition, one contribution compared a mega-analysis of family-based and population-based data to meta-analysis. Finally, the power of existing family-based methods for binary traits was compared. We conclude with suggestions for open research questions.