Recent years have witnessed significant research efforts in flexible organic and amorphous-metal-oxide analogue electronics, in view of its formidable potential for applications such as smart sensor systems. This Element provides a comprehensive overview of this growing research area. After discussing the properties of organic and amorphous-metal-oxide technologies relevant to analogue circuits, this Element focuses on their application to two key circuit blocks: amplifiers and analogue-to-digital converters. The Element thus provides a fresh look at the evolution and immediate opportunities of the field, and identifies the remaining challenges for these technologies to become the platform of choice for flexible analogue electronics.