A key approach to studying topological manifolds is decomposing them into smaller submanifolds using special fibrations such as "open book decompositions". An open book decomposition of an $n$-manifold (the open book) is a fibration that helps us study our manifold in terms of its ($n-1$)-dimensional fibers (the pages) and ($n-2$)-dimensional boundary of these submanifolds (the binding). Open books offer a powerful framework for analyzing special odd-dimensional smooth manifolds (contact manifolds). These fibrations shift the study of "contact manifolds" to a topological perspective. For example, every contact $3$-manifold can be represented as an open book, where the pages are surfaces and the binding is a knot or link. This talk explores higher-dimensional contact manifolds, examining their topological and geometric properties via open books, and discusses recent and ongoing research on fibrations with special singularities (Morse and Morse-Bott singularities).