This dissertation explored important issues of adaptive multiple testing problems. In Chapter 2, we showed that a class of dynamic adaptive procedures provides conservative point estimations for the proportion of true null hypotheses and FDR. These procedures are truly adaptive procedures because of their ability to adapt to the data when estimating null proportion. Thus, the dynamic adaptive procedures offer a solution to the problem of choosing the tuning parameters for adaptive procedures. In Chapter 3, we discussed important issues of gene set testing, which are commonly used in biological research, and the related multiple testing problems. We developed new methodology based on a hidden Markov model to test multiple gene sets of the Gene Ontology. Our method not only honors the logical relationships among the null hypotheses but also uses them to achieve more powerful results than other existing methods. In a sense, our method is able to adapt to dependences among null hypotheses to make better inference. In Chapter 4, we developed a more computationally efficient method to implement our hidden Markov methodology.