In this paper we introduce the concept of metasurfaces which are fully transparent when looking from one of the two sides of the sheet and have controllable functionalities for waves hitting the opposite side (one-way transparent sheets). We address the question on what functionalities are allowed, considering limitations due to reciprocity and passivity. In particular, we have found that it is possible to realize one-way transparent sheets which have the properties of a twist polarizer in transmission when illuminated from the other side. Also, active one-way transparent sheets with controllable copolarized reflection and transmission from the opposite side are feasible. We show that particular nonreciprocal magnetoelectric coupling inside the sheet is necessary to realize lossless nonactive transparent sheets. Furthermore, we derive the required polarizabilities of constituent dipole particles such that the layers composed of them form one-way transparent sheets. We conclude with design and simulations of an example of a nonreciprocal one-way transparent sheet functioning as an isolating twist polarizer.