Abstract
This note surveys two fundamental tools that unlock several topological properties of contact and symplectic manifolds; open book decompositions and Lefschetz fibrations. In particular, we will focus on planar contact manifolds, those that correspond to an open book decomposition with genus zero pages, and provide some fundamental results concerning planar open book decompositions and planar Lefschetz fibrations. We also introduce a higher-dimensional notion of planarity, iterated planarity as in [2], and present an exposition of generalizations of some of those results to higher dimensions.
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