The large-scale multiple testing problems resulting from the measurement of thousands of genes in microarray experiments have received increasing interest during the past several years. This article describes some commonly used criteria for controlling false positive errors, including familywise error rates, false discovery rates and false discovery proportion rates. Various statistical methods controlling these error rates are described. The advantages and disadvantages of these methods are discussed. These methods are applied to gene expression data from two microarray studies and the properties of these multiple testing procedures are compared.