Texture synthesis methods based on patch sampling and pasting that can generate realistic textures with a similar appearance to a small sample. However, the sample usually has to be used throughout the synthesis stage. In contrast, the learnt representation of the textures are more compact and discriminative, and can also yield good synthesis results. In this paper, we introduce a learnt approach for texture synthesis based on Support Vector Machines (SVM). This approach benefits from the merit of SVM that the sample texture pattern is learnt using a model, and the sample itself can be discarded during the synthesis stage; the approach is also used to synthesize 3D surface textures. Experimental results show that our approach is particularly effective in modeling and synthesizing nearregular or regular textures, which are difficult to achieve using traditional parametric texture synthesis methods. We further apply the proposed approach to constrained texture synthesis, image extrapolation and texture inpainting. For texture inpainting, we especially develop a new method for automatically detecting holes in textures without the requirement of human intervention. Our approach yields promising results for the three tasks.