This is an expository paper describing 
the role of the universal A-dynamical 
system in noncommutative dynamics.  In 
particular, we discuss its relationship 
to continuous free products of C*-algebras 
and its role in the dilation theory of 
quantum dynamical semigroups.  

Noncommutative moment polynomials are 
introduced, and their connection with 
dilation theory and $\alpha$-expectations 
are described.