The development of flexible and conformable devices, whose performance can be maintained while being continuously deformed, provides a significant step towards the realization of next-generation wearable and e-textiles applications. Organic field-effect transistors (OFETs) are particularly interesting for flexible and lightweight products, because of their low-temperature solution processability, and the mechanical flexibility of organic materials that endows OFETs the natural compatibility with plastic and biodegradable substrates. Here, an in-depth review of two competing flexible OFET technologies, planar and vertical OFETs (POFETs and VOFETs, respectively) is provided. The electrical, mechanical, and physical properties of POFETs and VOFETs are critically discussed, with a focus on four pivotal applications (integrated logic circuits, light-emitting devices, memories, and sensors). It is pointed out that the flexible function of the relatively newer VOFET technology, along with its perspective on advancing the applicability of flexible POFETs, has not been reviewed so far, and the direct comparison regarding the performance of POFET- and VOFET-based flexible applications is most likely absent. With discussions spanning printed and wearable electronics, materials science, biotechnology, and environmental monitoring, this contribution is a clear stimulus to researchers working in these fields to engage towards the plentiful possibilities that POFETs and VOFETs offer to flexible electronics. This article is protected by copyright. All rights reserved.