We present a new method for finding video CNN architectures that capture rich spatio-temporal information in videos. Previous work, taking advantage of 3D convolutions, obtained promising results by manually designing video CNN architectures. We here develop a novel evolutionary search algorithm that automatically explores models with different types and combinations of layers to jointly learn interactions between spatial and temporal aspects of video representations. We demonstrate the generality of this algorithm by applying it to two meta-architectures, obtaining new architectures superior to manually designed architectures: EvaNet. Further, we propose a new component, the iTGM layer, which more efficiently utilizes its parameters to allow learning of space-time interactions over longer time horizons. The iTGM layer is often preferred by the evolutionary algorithm and allows building cost-efficient networks. The proposed approach discovers new and diverse video architectures that were previously unknown. More importantly they are both more accurate and faster than prior models, and outperform the state-of-the-art results on multiple datasets we test, including HMDB, Kinetics, and Moments in Time. We will open source the code and models, to encourage future model development at https://sites.google.com/corp/view/evanet-video. .