Physarum polycephalum, commonly known as slime mold, is a large single-celled, multi-nucleated protist. As it searches for and exploits food sources, slime mold’s amoeboid movement and network-like structure exhibit intelligent behavior such as maze-solving and network optimization. To explore the mechanisms behind this brainless intelligence we explore two models. The Reaction-Diffusion-Advection model attempts to describe the rhythmic contractions, chemical oscillations, and pattern formation observed in the plasmodium of slime mold. The Current Reinforcement model attempts to replicate the network formation and optimization of slime mold. Together these micro- and macro-level models can describe the known behavior of slime mold and suggest the possible mechanisms and methods that propel its surprising intelligence.