Is it possible to restructure the non-linear activation functions in a deep network to create hardware-efficient models? To address this question, we propose a new paradigm called Restructurable Activation Networks (RANs) that manipulate the amount of non-linearity in models to improve their hardware-awareness and efficiency. First, we propose RAN-explicit (RAN-e) -- a new hardware-aware search space and a semi-automatic search algorithm -- to replace inefficient blocks with hardware-aware blocks. Next, we propose a training-free model scaling method called RAN-implicit (RAN-i) where we theoretically prove the link between network topology and its expressivity in terms of number of non-linear units. We demonstrate that our networks achieve state-of-the-art results on ImageNet at different scales and for several types of hardware. For example, compared to EfficientNet-Lite-B0, RAN-e achieves a similar accuracy while improving Frames-Per-Second (FPS) by 1.5x on Arm micro-NPUs. On the other hand, RAN-i demonstrates up to 2x reduction in #MACs over ConvNexts with a similar or better accuracy. We also show that RAN-i achieves nearly 40% higher FPS than ConvNext on Arm-based datacenter CPUs. Finally, RAN-i based object detection networks achieve a similar or higher mAP and up to 33% higher FPS on datacenter CPUs compared to ConvNext based models. The code to train and evaluate RANs and the pretrained networks are available at https://github.com/ARM-software/ML-restructurable-activation-networks.