In functional neuroimaging experiments, participants perform a set of tasks while their brain activity is recorded, e.g. with electroencephalography (EEG), magnetoencephalography (MEG) or functional magnetic resonance imaging (fMRI). Analysing data from a group of participants, which is often denoted as group-level analysis, aims at identifying traits in the data that relate with the tasks performed by the participant and that are invariant within the population. This allows understanding the functional organization of the brain in healthy subjects and its dysfunctions in pathological populations. While group-level analyses for classical univariate statistical inference schemes, such as the general linear model, have been heavily studied, there are still many open questions for group-level strategies based on multivariate machine learning methods. This thesis therefore focuses on multivariate group-level analysis of functional neuroimaging and brings four contributions. The first contribution is a comparison of the results provided by two classifier-based multivariate group-level strategies: i) the standard one in which one aggregates the performances of within-subject models in a hierarchical analysis, and ii) the scheme we denote as inter-subject pattern analysis, where a population-level predictive model is directly estimated from data recorded on multiple subjects. An extensive set of experiments are conducted on both a large number of artificial datasets - where we parametrically control the size of the multivariate effect and the amount of inter-individual variability - as well as on two real fMRI datasets. Our results show that the two strategies can provide different results and that inter-subject analysis both offers a greater ability to small multivariate effects and facilitates the interpretation of the obtained results at a comparable computational cost. We then provide a survey of the methods that have been proposed to improve inter-subject pattern analysis, which is actually a hard task due to the largely heterogeneous vocabulary employed in the literature dedicated to this topic. Our second contribution consists in first introducing an unifying formalization of this framework, that we cast as a multi-source transductive transfer learning problem, and then in reviewing more than 500 related papers to offer a first comprehensive view of the existing literature where inter-subject pattern analysis was used in task-based functional neuroimaging experiments. Our third contribution is an experimental study that examines the well-foundedness of our multi-source transductive transfer formalization of inter-subject pattern analysis. With fMRI and MEG data recorded from numerous subjects, we demonstrate that between-subject variability impairs the generalization ability of classical machine learning algorithms and that a standard multi-source transductive learning strategy improves the generalization performances of such algorithms. Based on these promising results we further investigate the use of two more advanced machine learning methods to deal with the multi-source problem. The fourth contribution of this thesis is a new multivariate group-level analysis method for functional neuroimaging datasets. Our method is based on optimal transport, which leverages the geometrical properties of multivariate brain patterns to overcome inter-individual differences impacting the traditional group-level analyses. We extend the concept of Wasserstein barycenter, which was initially meant to average probability measures, to make it applicable to arbitrary data that do not necessarily fulfill the properties of a true probability measure. For this, we introduce a new algorithm that estimates a barycenter and provide an experimental study on artificial and real functional MRI.