We will discuss the renormalization-group evolution of several types of theories, both asymptotically free and infrared-free: (i) an analysis of asymptotically free non-abelian gauge theories with various fermion contents, including higher-loop calculations of the IR zero of the beta function and anomalous dimension of the fermion bilinear, and comparison with lattice measurements; (ii) an investigation of a possible UV zero of the beta function for a U(1) gauge theories up to five-loop order; (iii) a similar study for an O(N) λ |φ|⁴ theory up to five-loop order; and (iv) an analysis of the RG flow diagram for a Yukawa theory in the space of quartic and Yukawa couplings. We also discuss scheme transformations and their effect on a zero of the beta function calculated to higher-loop order.