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The aim in this paper is to give expressions for modular linear differentialoperators of any order. In particular, we show that they can all be describedin terms of Rankin-Cohen brackets and a modified Rankin-Cohen bracket found byKaneko and Koike. We also give more uniform descriptions of MLDOs in terms ofcanonically defined higher Serre derivatives and an extension of Rankin-Cohenbrackets, as well as in terms of quasimodular forms and almost holomorphicmodular forms. The last of these descriptions involves the holomorphicprojection map. The paper also includes some general results on the theory ofquasimodular forms on both cocompact and non-cocompact subgroups of$SL_2(\mathbb{R})$, as well as a slight sharpening of a theorem of Martin andRoyer on Rankin-Cohen brackets of quasimodular forms

Modular Linear Differential Operators and Generalized Rankin-Cohen Brackets