Recently, there have been tremendous efforts in developing lightweight Deep Neural Networks (DNNs) with satisfactory accuracy, which can enable the ubiquitous deployment of DNNs in edge devices. The core challenge of developing compact and efficient DNNs lies in how to balance the competing goals of achieving high accuracy and high efficiency. In this paper we propose two novel types of convolutions, dubbed Pixel Difference Convolution (PDC) and Binary PDC (Bi-PDC) which enjoy the following benefits: capturing higher-order local differential information, computationally efficient, and able to be integrated with existing DNNs. With PDC and Bi-PDC, we further present two lightweight deep networks named Pixel Difference Networks (PiDiNet) and Binary PiDiNet (Bi-PiDiNet) respectively to learn highly efficient yet more accurate representations for visual tasks including edge detection and object recognition. Extensive experiments on popular datasets (BSDS500, ImageNet, LFW, YTF, etc.) show that PiDiNet and Bi-PiDiNet achieve the best accuracy-efficiency trade-off. For edge detection, PiDiNet is the first network that can be trained without ImageNet, and can achieve the human-level performance on BSDS500 at 100 FPS and with 1 M parameters. For object recognition, among existing Binary DNNs, Bi-PiDiNet achieves the best accuracy and a nearly 2× reduction of computational cost on ResNet18.