The review covers modern directions of the implementation of high-resolution continuous-source electrothermal atomic absorption spectrometry (HR CS ETAAS) for quantitative analysis. Approaches to the direct analysis of solid samples of various compositions, including determination using aqueous reference solutions, analysis of suspensions and sorbates after sorption separation, use of various modifiers, and optimization of the program of heating graphite furnace are systematized. Restrictions of HR CS ETAAS in the determination of poorly volatile elements are noted, methods for increasing the rate of their atomization in a graphite furnace are described. The potentials of HR CS ETAAS for the simultaneous and consecutive monitoring of atomic lines are investigated. The difference between the simultaneous multielement determination and consecutive determination in one aliquot portion is noted. Restrictions of simultaneous multielement analysis by HR CS ETAAS in the number of elements, their thermochemical properties, and intensities of corresponding absorption lines are described. Possibilities of molecular absorption spectrometry for the determination of analytes whose atomic absorption lines are outside the continuous spectrum range of 190–900 nm are discussed. A promising approach to the determination of sulfur, phosphorus, halogens, and aluminum by absorption lines of diatomic molecules is presented.