Flexible transport systems such as Demand Responsive Transit (DRT) are becoming more and more popular over the last few years due to their convenience for customers. However, this convenience comes at a price. Transport authorities are currently looking for ways to improve service flexibility of Conventional Public Transport (CPT), which is undoubtedly cheaper than DRT. This justifies the need for Flex-Route Transit (FRT), which combines the flexibility of DRT and the low cost of CPT. This paper surveys research developments on FRT, as a promising alternative mode of public transport. Based on this survey, we discuss current research gaps that may be filled to increase FRT applicability. Moreover, we show how literature on classic Operations Research problems is of help to do so. In particular, we study similarities and differences between FRT and Vehicle Routing Problem, and specifically with one of its variant named Dial-a-Ride Problem. The analysis illustrates promising techniques that may be of use for solving FRT.