The weak-type (1,1) estimate for Calderón-Zygmund operators is essential in harmonic analysis. This estimate was originally proved using the Calderón-Zygmund decomposition. To address more general settings, Nazarov, Treil, and Volberg gave a different proof of the weak-type (1,1) estimate. We investigate this proof technique. A comparison between the Calderón-Zygmund decomposition and Nazarov-Treil-Volberg techniques, a simplification of the Nazarov-Treil-Volberg proof in the classical setting, and applications in weighted and multilinear settings will be discussed.