Thanks to the extraordinary advances flexible electronics have experienced over the last decades, applications such as conformable active-matrix displays, ubiquitously integrated disposable flexible sensor nodes, wearable or textile-integrated systems, as well as imperceptible and transient implants are now reachable. To enable these applications, specialized analog circuits able to transmit and receive data, condition sensors' parameters, drive actuators or control powering devices are required. High-performance sensor conditioning, driving and transceiver circuits on a wide range of flexible substrates are therefore extremely important to develop. However, the currently available materials and processes compatible with mechanically flexible substrates impose massive limitations in terms of large-area uniformity, device dimensions' shrinkability and circuit design, challenging the realization of flexible analog systems. Among state-of-the-art technologies employing low-temperature fabrication processes, thin-film transistors (TFTs) based on metal oxide semiconductors represent the potentially best compromise in terms of prize, performance, technology maturity and capacity to realize complex systems. This is why metal oxide TFTs are nowadays widely used for flexible, light-weight, transparent, stretchable and bio-degradable analog circuits and systems. Here, we review the current trends of flexible metal oxide TFTs for analog applications. First, an introduction is given, where current challenges and requirements related to the realization of flexible analog circuits and systems are analysed. Additionally, TFT performance parameters and configurations are briefly revised. Then, the recent advances in the field of flexible metal oxide TFTs for analog applications are summarized. In particular, all reported approaches to reduce the channel length and improve the AC performance are shown. Next, the current state of flexible metal oxide TFT-based analog circuits is shown, discussing n-type only and complementary circuit configurations. The last topic of the review covers systems based on flexible metal oxide analog circuits. Finally, a conclusion is drawn and an outlook over the field is provided.