Electrically thin composite layers (metasurfaces) can be used to shape transmitted fields. It is usually desirable that reflections from the metasurface are absent, while the phase of the transmission coefficient can be fully controlled by tuning the metasurface structure. More generally, it is desirable to shape both the phase and amplitude of transmitted waves, still allowing no reflections. In this presentation we discuss necessary physical conditions for realizing these properties, both for normal and oblique illuminations, and present examples of new topologies of metasurfaces for control of transmitted waves.