The genetic nature of psychiatric disorders was observed by clinicians long before DNA had been identified as the molecule of inheritance. The greatest identified risk factor of many psychiatric disorders still is a positive family history. Until recently this knowledge has not contributed substantially to treatment efforts or to a better understanding of the disease processes because we lacked the necessary genetic data. Advances in genotyping technologies have brought an end to this data shortage which is leading to a better understanding of the genetic architecture of psychiatric disorders. Two patterns started to emerge which were uncommon in earlier studied Mendelian disorders. (i) most of the genetic part of disease risk is conferred by a large number of genetic loci of small effect, and (ii) genetic loci often influence a large number of traits at the same time. While this is true of many traits ("complex" traits), these two phenomena (polygenicity and pleiotropy) are particularly pronounced in psychiatric disorders. This has wide-reaching consequences for the analysis and interpretation of genetic data and provides challenges as well as opportunities. This thesis focuses on two areas in particular: genetic heterogeneity and genetic risk prediction.Genetic heterogeneity in a phenotypically homogenous group describes a situation where different and distinct genetic risk profiles are causing similar symptoms in different people.This can be easily identified under a Mendelian inheritance pattern, but proves to be challenging under polygenicity. The presence of genetic heterogeneity can limit the accuracy of genetic risk prediction.The aim of genetic risk prediction is to use the information that has been gathered on the effects of genetic loci to estimate the genetic liability of an individual to develop a disease.Here, pleiotropy offers an opportunity to increase the accuracy of genetic prediction by leveraging information from multiple diseases at the same time.The aim in this thesis is to describe several projects which center around the two concepts of genetic risk prediction based on multiple traits and of genetic heterogeneity. Chapter 1 sets the scene with an overview of recently developed polygenic methods. Chapter 2 deals with the effects of genetic heterogeneity on heritability estimates and demonstrates how genetic heterogeneity might contribute to the phenomenon of missing heritability, which is 3 the discrepancy between twin study heritability estimates and the variance explained by the sum of individual genetic loci. Chapter 3 addresses the question of whether genotype clustering can detect groups with different genetic risk profiles. Chapter 4 describes the implementation of a multivariate extension to the univariate Best Linear Unbiased Prediction (BLUP) method and its application to five psychiatric traits. Chapters 4 and 5 investigate whether this multivariate BLUP model can be approximated when only summary statistics, not individual level genotype data, are available for the predi...