  We discuss some general aspects of renormalization group flows in four
dimensions. Every such flow can be reinterpreted in terms of a spontaneously
broken conformal symmetry. We analyze in detail the consequences of trace
anomalies for the effective action of the Nambu-Goldstone boson of broken
conformal symmetry. While the c-anomaly is algebraically trivial, the a-anomaly
is "non-Abelian," and leads to a positive-definite universal contribution to
the S-matrix of 2->2 dilaton scattering. Unitarity of the S-matrix results in a
monotonically decreasing function that interpolates between the Euler anomalies
in the ultraviolet and the infrared, thereby establishing the a-theorem.
