For the etiology, progression, and treatment of complex diseases, gene-environment (G-E) interactions have important implications beyond the main G and E effects. G-E interaction analysis can be more challenging with the higher dimensionality and need for accommodating the "main effects, interactions" hierarchy. In the recent literature, an array of novel methods, many of which are based on the penalization technique, have been developed. In most of these studies, however, the structures of G measurements, for example the adjacency structure of SNPs (attributable to their physical adjacency on the chromosomes) and network structure of gene expressions (attributable to their coordinated biological functions and correlated measurements), have not been well accommodated. In this study, we develop the structured G-E interaction analysis, where such structures are accommodated using penalization for both the main G effects and interactions. Penalization is also applied for regularized estimation and selection. The proposed structured interaction analysis can be effectively realized. It is shown to have the consistency properties under high dimensional settings. Simulations and the analysis of GENEVA diabetes data with SNP measurements and TCGA melanoma data with gene expression measurements demonstrate its competitive practical performance. This article is protected by copyright. All rights reserved.