The recent focus on genetic rare variants has produced a large number of testing strategies to assess association between a group of rare variants and a heritable trait, with competing claims about the performance of various tests. We review frequently used tests and show that they fall into either linear or quadratic classes, and neither class consistently outperforms the other across genetic models (Derkach, Lawless and Sun online, Statistical Science). This understanding leads to development of robust tests that borrow strength from the two complementary classes (Derkach, Lawless and Sun 2013, Genetic Epidemiology). However, regardless of the specific test used, power is generally low in current realistic settings due to various factors including rareness of the key variants and multiple hypothesis testing. To increase power, we investigate various cost-effective response-dependent sampling strategies. This is joint work with graduate student Andriy Derkach and Professor Jerry Lawless.