We describe the design, construction, and operation of a versatile dual-species Zeeman slower for both Cs and Yb, which is easily adaptable for use with other alkali metals and alkaline earths. With the aid of analytic models and numerical simulation of decelerator action, we highlight several real-world problems affecting the performance of a slower and discuss effective solutions. To capture Yb into a magneto-optical trap(MOT), we use the broad ¹S0 to ¹P1 transition at 399 nm for the slower and the narrow ¹S0 to ³P1 intercombination line at 556 nm for the MOT. The Cs MOT and slower both use the D2 line (6²S1/2 to 6²P3/2 at 852 nm. The slower can be switched between loading Yb or Cs in under 0.1 s. We demonstrate that within a few seconds the Zeeman slower loads more than 10⁹ Yb atoms and 10⁸ Cs atoms into their respective MOTs. These are ideal starting numbers for further experiments on ultracold mixtures and molecules.