For nearly 50 years, the mechanism by which microtubules are organized in eukaryotic cells has challenged researchers. In animal cells, the centriole-based centrosome acts as a central microtubule organizing centre and confines assembly of microtubule arrays to spindle poles, perinuclear radial arrays and flagella. Plant cells lack centrosomes and microtubules are far more dispersed, especially during interphase when arrays form at the cell cortex that consist of many disconnected yet highly ordered microtubules. The parallel organization of these cortical arrays is essential for the unidirectional growth of plant cells, with the axis of elongation running perpendicular to the predominant microtubule orientation. In this seminar I will outline recent research we have conducted to understand the mechanisms that drive spatial organization of the plant cortical array. Using a combination of genetic strategies, live cell imaging and computational simulations, we have identified the dynamic parameters required to establish both parallel order in 2 dimensions and hava also discovered how cell geometry and the unique properties of one microtubule associated protein determine how microtubule orientation is controlled in 3-dimension on all faces of polyhedral plant cells.