In this thesis, methods for texture mapping voxel based terrain of arbitrary topology, are studied. Traditional methods for generating terrain often use 2D height maps which has its limitations in topology, but often can rely on fast and simple planar projection for texture mapping. To generate terrain of arbitrary topology and support features like caves, overhangs and vertical cliffs, the terrain representation needs to expand from two dimensions and surface rendering to three dimensions and volumetric rendering, and also needs other, more elaborate methods for texture mapping. The initial part of the thesis recounts \emph{Marching Cubes}, the main method used for volumetric rendering, and also some basics on texture mapping. A survey reviews different related work on the area and lists some of the features. Some initial tests, to achieve texture mapping on arbitrary terrain, are performed and are explained and evaluated. These tests focus on partition the terrain into submeshes of similar directional faces, using the initial voxel grid as a natural boundary, and project each submesh to a planar texture space called \emph{charts}. The texture of each chart is defined by the highest resolution of each submesh and all charts are stored in one \emph{texture atlas}. The charts then represent the texture used for all different resolutions of the submesh. The method results in gaps in the final texture due to mismatch occurring from the different mesh resolutions. To avoid the mismatch each chart is mapped to fixed shapes, namely triangles or quads. This solves the problem with gaps along chart boundaries but instead introduce heavy distortion in the texture due to stretching and resizing. Some tests have also been performed on editing the underlying scalar field directly by identifying and avoiding some unwanted cases, and creating a simpler mesh.