The data generated by high-throughput biotechnologies are characterized by their high-dimension and heterogeneity. Usual, tried and tested inference approaches are questioned in the statistical analysis of such data. Motivated by issues raised by the analysis of gene expressions data, I focus on the impact of dependence on the properties of multiple testing procedures in high-dimension. This article aims at presenting the main results: after introducing the issues brought by dependence among variables, the impact of dependence on the error rates and on the procedures developed to control them is more particularly studied. It results in the description of an innovative methodology based on a factor structure to model the data heterogeneity, which provides a general framework to deal with dependence in multiple testing. The proposed framework leads to less variability for error rates and consequently shows large improvements of power and stability of simultaneous inference with respect to existing multiple testing procedures. Besides, the model parameters estimation in a high-dimensional setting and the determination of the number of factors to be considered in the model are evoked. These results are then illustrated by real data from microarray experiments analyzed using the R package called FAMT. This paper is an extended written version of my oral presentation on the same topic at the 44th Journées de Statistique organized by the French Statistical Society (SFdS) in Bruxelles, Belgium, 2012, when being awarded the Marie-Jeanne Laurent-Duhamel prize.