This study shows that AlSi10Mg parts with an extremely fine microstructure and a controllable texture can be obtained through Selective Laser Melting (SLM). Selective Laser Melting creates complex functional products by selectively melting powder particles of a powder bed layer after layer using a high energy laser beam. The high energy density applied to the material and the additive character of the process results in a unique material structure. To investigate this material structure, cube-shaped SLM parts were made using different scanning strategies and investigated by microscopy, X-ray diffraction and electron backscattered diffraction. The experimental results show that the high thermal gradients occurring during SLM lead to a very fine microstructure with submicron sized cells. Consequently, the AlSi10Mg SLM products have a high hardness of 127 ± 3 Hv0.5 even without the application of a precipitation hardening treatment. Furthermore, due to the unique solidification conditions and the additive character of the process, a morphological and crystallographic texture is present in the SLM parts. Thanks to the knowledge gathered in this article on how this texture is formed and how it depends on the process parameters, this texture can be controlled. A strong fibrous <100> texture can be altered into a weak cube texture along the building and scanning directions when a rotation of 90° of the scanning vectors within or between the layers is applied.