Plant microtubules (MTs) polymerize and depolymerize in a process termed dynamic instability. This allows the assembly, reorganization, and disassembly of at least four MT arrays throughout the cell cycle. The cortical MT array lines the plasma membrane during interphase and plays a central role in directional cell expansion. Microtubule-associated proteins (MAPs) decorate cortical MTs with distinct patterns, regulating MT dynamic instability, MT severing, and other array-ordering processes. The Arabidopsis root has emerged as a highly useful system for identifying and studying cell-expansion-related MAPs. Here, we review how cortical MTs are thought to behave and become ordered in expanding root cells, and we discuss the emerging picture of how MAPs fundamentally govern MT ordering and directional growth processes.