Topology optimization is a numerical method to find the optimal distribution of a given amount of material that maximizes the performance of the resulting structure, which is subjected to boundary conditions that include external forces and heat loads. An effective approach to solve a topology optimization problem is the use of the level set method. In this method, the boundary of an n-dimensional structure is defined as the zero level set map of a (n+1)-dimensional surface. Benefits of the level set method include an easily adaptive topology, the ability to set parameters that change complexity of the resulting object, and speed of the code. Drawbacks include intermittent re-initialization of the level set function and ill-posed, steady state solutions. This work studies various implementations of the level set method and compare them to traditional density-based methods, which are widely used in topology optimization.