We exploit topological semimetallic phases resulting from the Kondo screening in Anderson lattice models. It is shown that by including spin-orbit interactions both in the bulk electrons and in the hybridization between the conduction electrons and electrons in the f orbit, all types of topological semimetallic phases can be realized in Anderson lattice models. Specifically, upon either broken time-reversal symmetry or broken inversion symmetry, we find that either the Weyl semimetallic phase, Dirac semimetallic phase, or nodal-ring semimetallic phases always emerge between insulating phases and can be accessed by tuning either temperature or spin-orbit interaction. For Anderson lattice models with general three-dimensional spin-orbit hybridization between the conduction electrons and electrons in the f orbit, we find that Weyl nodal-ring semimetallic phases emerge between strong and weak topological insulating phases. Furthermore, in the presence of an exchange field, Weyl semimetallic phases form after two Weyl points of charge ±1 split off from a Dirac point at time-reversal momenta. On the other hand, when the spin-orbit interaction is included in the conduction electron, we find that upon the rotation symmetry being broken with anisotropic hopping amplitudes, a Weyl semimetallic phase emerges with a double Weyl node with charges of ±2. Furthermore, the Weyl semimetallic phases with charges of ±2 can be tuned into Weyl semimetallic phases with charges of ±1 through the inclusion of the Rashba spin-orbit interaction. Our analyses indicate that Anderson lattices with appropriate spin-orbit interactions provide a platform for realizing all types of topological semimetallic phases.