Significance testing was developed as an objective method for summarizing statistical evidence for a hypothesis. It has been widely adopted in genetic studies, including genome-wide association studies and, more recently, exome sequencing studies. However, significance testing in both genome-wide and exome-wide studies must adopt stringent significance thresholds to allow multiple testing, and it is useful only when studies have adequate statistical power, which depends on the characteristics of the phenotype and the putative genetic variant, as well as the study design. Here, we review the principles and applications of significance testing and power calculation, including recently proposed gene-based tests for rare variants.