  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 reflection or
transmission when illuminated from the other side. Also one-way transparent
sheets with controllable co-polarized reflection and transmission from the
opposite side are feasible. We show that particular non-reciprocal
magneto-electric coupling inside the sheet is necessary to realize lossless
non-active 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.
