To search the entire human genome for association is a novel and promising approach to unravelling the genetic basis of complex genetic diseases. In these genome-wide association studies (GWAs), several hundreds of thousands of single nucleotide polymorphisms (SNPs) are analyzed at the same time, posing substantial biostatistical and computational challenges. In this paper, we discuss a number of biostatistical aspects of GWAs in detail. We specifically consider quality control issues and show that signal intensity plots are a sine qua condition non in todays GWAs. Approaches to detect and adjust for population stratification are briefly examined. We discuss different strategies aimed at tackling the problem of multiple testing, including adjustment of p-values, the false positive report probability and the false discovery rate. Another aspect of GWAs requiring special attention is the search for gene-gene and gene-environment interactions. We finally describe multistage approaches to GWAs.