The use of flexible sensors has tripled over the last decade due to the increased demand in various fields including health monitoring, food packaging, electronic skins and soft robotics. Flexible sensors have the ability to be bent and stretched during use and can still maintain their electrical and mechanical properties. This gives them an advantage over rigid sensors that lose their sensitivity when subject to bending. Advancements in 3D printing have enabled the development of tailored flexible sensors. Various additive manufacturing methods are being used to develop these sensors including inkjet printing, aerosol jet printing, fused deposition modelling, direct ink writing, selective laser melting and others. Hydrogels have gained much attention in the literature due to their self-healing and shape transforming. Self-healing enables the sensor to recover from damages such as cracks and cuts incurred during use, and this enables the sensor to have a longer operating life and stability. Various polymers are used as substrates on which the sensing material is placed. Polymers including polydimethylsiloxane, Poly(N-isopropylacrylamide) and polyvinyl acetate are extensively used in flexible sensors. The most widely used nanomaterials in flexible sensors are carbon and silver due to their excellent electrical properties. This review gives an overview of various types of flexible sensors (including temperature, pressure and chemical sensors), paying particular attention to the application areas and the corresponding characteristics/properties of interest required for such. Current advances/trends in the field including 3D printing, novel nanomaterials and responsive polymers, and self-healable sensors and wearables will also be discussed in more detail.