The rapid growth of molecular biology and neuroimaging has facilitated many massive imaging genetics studies. These studies greatly advance our understanding of the development of neuropsychiatric and neurodegenerative disorders and their relationships to genetic biomarkers. Among the various collected structural and functional imaging data, we are particularly interested in those observed over time and/or space domains. One powerful type of statistical approach to analyze this kind of imaging data is based on functional data analysis techniques, including varying coefficient approaches and functional linear regression. This work improves functional data analysis approaches to imaging data by incorporating genetic information in the model which therefore improves explanatory and predictive power available from massive imaging genetics datasets. We propose two novel functional regression models for imaging genetics data, a semi-nonparametric varying coefficient model with functional response and a partially functional linear regression model with high-dimensional component. The performances of both models are assessed via extensive simulation studies. These methods are also applied to analyze real data collected in large imaging genetics studies such as the Alzheimer's Disease Neuroimaging Initiative and the Philadelphia Neurodevelopmental Cohort.