  We present a framework to treat quantum networks and all possible
transformations thereof, including as special cases all possible manipulations
of quantum states, measurements, and channels, such as, e.g., cloning,
discrimination, estimation, and tomography. Our framework is based on the
concepts of quantum comb-which describes all transformations achievable by a
given quantum network-and link product-the operation of connecting two quantum
networks. Quantum networks are treated both from a constructive point of
view-based on connections of elementary circuits-and from an axiomatic
one-based on a hierarchy of admissible quantum maps. In the axiomatic context a
fundamental property is shown, which we call universality of quantum memory
channels: any admissible transformation of quantum networks can be realized by
a suitable sequence of memory channels. The open problem whether this property
fails for some nonquantum theory, e.g., for no-signaling boxes, is posed.
