Twenty-five years ago, the two main pillars of quantum chemistry—density functional and composite ab initio theories—were recognized with a Nobel Prize in Chemistry awarded to Walter Kohn and John Pople. This recognition sparked intense theoretical developments in both fields. Whereas in 1998, the year the Nobel Prize was awarded, there were only a handful of composite ab initio methods; most notably the Gaussian-n methods (n = 1–3), CBS methods (e.g., CBS-QCI and CBS-APNO), and the focal-point analysis approach, today there are many more families of such methods, including the Weizmann-n, MCCM, HEAT, ccCA, FPD, ATOMIC, INT-MP2-F12, and ChS family of methods, where some of these families include dozens of variants. Overall, there are over 100 contemporary variants of composite ab initio methods to choose from, with many variants implemented as a keyword in popular quantum chemical packages. This situation makes it difficult to choose a proper method for a given chemical system, property, and desired accuracy. This chapter provides an overview of contemporary composite ab initio methods applicable to first- and second-row elements, their main energetic components, and their expected accuracy and applicability. To guide the selection of a suitable method for a given chemical system and desired accuracy, the various methods are classified according to a ‘Jacob's Ladder’ of composite ab initio methods, from computationally economical methods that are capable of approaching chemical accuracy to computationally demanding methods capable of confident sub-benchmark accuracy.