We will introduce basic principles of cell cytoskeleton self-organization. We will show how surface micro-patterning can be used to impose spatial boundary conditions to the growth of cytoskeleton filaments such as actin and microtubules. This allowed to initiate the quantitative description and the formulation of the geometrical and mechanical rules directing cytoskeleton filaments self-organization. We will try to highlight the current challenges we foresee in this field and the need for more advanced investigation of the underlying physics principles. We will also discuss few technological developments that could benefit from the use of directed actin or microtubule self-organization, notably in the case of micro-electronics.