In the field of neuroimage analysis two key goals are to understand the association of a high- dimensional imaging variable with a phenotype, and to understand relationships between several high-dimensional imaging variables. Several recent studies have shown that the standard "mass- univariate" methods to test an association of an image with a phenotype have inflated type 1 error rates due to invalid assumptions. Here, we propose two new methods to perform association testing in neuroimaging and illustrate the method in two stages of the lifespan. The first is a parametric bootstrap testing procedure that estimates the joint distribution of test statistical parametric map in order to control the voxel-wise family-wise error rate (FWER). We illustrate the method by identifying sex differences in nonlinear developmental trajectories of cerebral blood flow through adolescence using the Philadelphia Neurodevelopmental Cohort. The second testing procedure is a generalization of Rao's score test based on projecting the score statistic onto a linear subspace of a high-dimensional parameter space. The approach provides a way to localize signal in the high-dimensional space by projecting the scores to the subspace where the score test was performed. This allows for inference in the high-dimensional space to be performed on the same degrees of freedom as the score test, effectively reducing the number of comparisons. We illustrate the method by analyzing a subset of the Alzheimer's Disease Neuroimaging Initiative dataset. Finally, we propose a new tool to study relationships between neuroimaging modalities that we to describe how the spatial association between cortical thickness and sulcal depth changes in adolescent development.