Convolutional neural networks are constructed with massive operations with different types and are highly computationally intensive. Among these operations, multiplication operation is higher in computational complexity and usually requires {more} energy consumption with longer inference time than other operations, which hinders the deployment of convolutional neural networks on mobile devices. In many resource-limited edge devices, complicated operations can be calculated via lookup tables to reduce computational cost. Motivated by this, in this paper, we introduce a generic and efficient lookup operation which can be used as a basic operation for the construction of neural networks. Instead of calculating the multiplication of weights and activation values, simple yet efficient lookup operations are adopted to compute their responses. To enable end-to-end optimization of the lookup operation, we construct the lookup tables in a differentiable manner and propose several training strategies to promote their convergence. By replacing computationally expensive multiplication operations with our lookup operations, we develop lookup networks for the image classification, image super-resolution, and point cloud classification tasks. It is demonstrated that our lookup networks can benefit from the lookup operations to achieve higher efficiency in terms of energy consumption and inference speed while maintaining competitive performance to vanilla convolutional networks. Extensive experiments show that our lookup networks produce state-of-the-art performance on different tasks (both classification and regression tasks) and different data types (both images and point clouds).