Additive Manufacturing (AM) is gaining popularity in aerospace and automotive industries. This is a versatile manufacturing process, where highly complex structures are fabricated and together with topology optimization, a powerful design tool, it shares the property of providing a very large freedom in geometrical form. The main focus of this work is to introduce new developments of Topology Optimization (TO) for metal AM. The thesis consists of two parts. The first part introduces background and theory, where TO and adjoint sensitivity analysis are described. Furthermore, methodology used to identify surface layer and high-cycle fatigue are introduced. In the second part, three papers are appended, where the first paper presents the treatment of surface layer effects, while the second and third papers provide high-cycle fatigue constraint formulations. In Paper I, a TO method is introduced to account for surface layer effects, where different material properties are assigned to bulk and surface regions. In metal AM, the fabricated components in as-built surface conditions significantly affect mechanical properties, particularly fatigue properties. Furthermore, the components are generally in-homogeneous and have different microstructures in bulk regions compared to surface regions. We implement two density filters to account for surface effects, where the width of the surface layer is controlled by the second filter radius. 2-D and 3-D numerical examples are treated, where the structural stiffness is maximized for a limited mass. For Papers II and III, a high-cycle fatigue constraint is implemented in TO. A continuous-time approach is used to predict fatigue-damage. The model uses a moving endurance surface and the development of damage occurs only if the stress state lies outside the endurance surface. The model is applicable not only for isotropic materials (Paper II) but also for transversely isotropic material properties (Paper III). It is capable of handling arbitrary load histories, including non-proportional loads. The anisotropic model is applicable for additive manufacturing processes, where transverse isotropic properties are manifested not only in constitutive elastic response but also in fatigue properties. Two optimization problems are solved: In the first problem the structural mass is minimized subject to a fatigue constraint while the second problem deals with stiffness maximization subjected to a fatigue constraint and mass constraint. Several numerical examples are tested with arbitrary load histories.