**Abstract**

Over the years, several optimization techniques were widely used to find the optimum shape and size of engineering structures (trusses, frames, etc.) under different constraints (stress, displacement, buckling instability, kinematic stability, and natural frequency). But, most of them require continuous data set where, on the other hand, topology optimization (TO) can handle also discrete ones. Topology optimization has also allowed radical changes in geometry which concludes better designs. So, many researchers have studied on topology optimization by developing/using different methodologies. This study aims to classify these studies considering used methods and present new emerging application areas. It is believed that researchers will easily find the related studies with their work.

**Keywords:** topology optimization, finite element method
