Capturing spatiotemporal dynamics is an essential topic in video recognition. In this paper, we present learnable higher-order operations as a generic family of building blocks for capturing spatiotemporal dynamics from RGB input video space. Similar to higher-order functions, the weights of higher-order operations are themselves derived from the data with learnable parameters. Classical architectures such as residual learning and network-in-network are first-order operations where weights are directly learned from the data. Higher-order operations make it easier to capture context-sensitive patterns, such as motion. Self-attention models are also higher-order operations, but the attention weights are mostly computed from an affine operation or dot product. The learnable higher-order operations can be more generic and flexible. Experimentally, we show that on the task of video recognition, our higher-order models can achieve results on par with or better than the existing state-of-the-art methods on Something-Something (V1 and V2), Kinetics and Charades datasets.