Over-the-air computation (AirComp) leverages the signal superposition characteristic of wireless multiple-access channels (MACs) to perform mathematical computations. Initially introduced to enhance communication reliability in interference channels and wireless sensor networks (WSNs), AirComp has more recently found applications in task-oriented communications like wireless distributed learning and in wireless control systems. Its adoption aims to address latency challenges arising from an increased number of edge devices or Internet of Things (IoT) devices accessing the constrained wireless spectrum. This article is the first one to focus on the physical layer (PHY) of these systems. We present a unified framework, specifically on the waveform and the signal processing aspects at the transmitter and receiver, to meet the challenges that AirComp presents within the different contexts and use cases.