In order to fulfill the demands of today’s society considering efficient use of natural resources and energy, structural components designed by engineers are pushed to being more efficient in its use of material and energy. Structural optimization is a tool that can aid engineers with this goal. There are three types of structural optimization, size-, shape-, and topology optimization. This report will focus on the latter. Topology optimization is a mathematical optimization technique that finds the best performing structure for given loads, constraints and boundary conditions, while not being limited by the initial input of the engineer geometry-wise. Engineering properties that can be included in a topology optimization problem are: compliance, volume, stress, eigenfrequency, buckling, and fatigue. There are three main methods for implementing TO problems. Which are homogenization method, SIMP method, level set method, and evolutionary methods. In order to be able to evaluate a broader spectrum of design problems, also nonlinear and dynamic theory can be incorporated. The nonlinearities that were investigated are geometric and material nonlinearities. Dynamic problems that were investigated include: free- and forced vibrations, general dynamic loading, and topology optimization of multibody systems. Considering the industrial implementation, the automobile and the aviation industry are investigated because they already have topology optimization incorporated into their design process. Generally, topology optimization is used in its ’classical’ form of compliance minimization, resulting in stiff and lightweight structures. The structure is subsequently re-designed with the topology optimization result in mind. Other engineering properties such as stress, are taken into account later in the design process, and may be optimized using size and shape optimization. In the domain of transport engineering, TO is already emerging as design tool. In the studied cases, it was used in the same way as in the other industries. Namely, as part of a two-step design process. First generating a stiff and lightweight structure using topology optimization, and later optimizing for other engineering properties. Dynamic structures are prominent in the domain of transport engineering, and benefit greatly from efficient material use. Therefore focus on applying topology optimization for such structures seems a logical choice. Furthermore, structures that are not intuitive to design can benefit from TO, since it is not so much dependent on engineers input.