Resumo: The topological derivative is defined as the first term (correction) of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of singular domain perturbations, such as holes, inclusions, source-terms and cracks (Novotny & Sokolowski, 2013). This relatively new concept has applications in many different fields such as shape and topology optimization, inverse problems, image processing, multi-scale material design and mechanical modeling including damage and fracture evolution phenomena. In this talk the topological derivative method is presented, together with a portfolio of applications in the context of topology design optimization of electromagnetic devices.