In this paper, the authors aim at unifying, simplifying, and improving the convergence rate analysis of Lagrangian-based methods for convex optimization problems. They first introduce the notion of nice primal algorithmic map, which plays a central role in the unification and in the simplification of the analysis of most Lagrangian-based methods. Equipped with a nice primal algorithmic map, they introduce a versatile generic scheme, which allows for the design and analysis of faster Lagrangian (FLAG) methods with new provably sublinear rate of convergence expressed in terms of function values and feasibility violation of the original (nonergodic) generated sequence. The most well@-known Lagrangian-based schemes admit nice primal algorithmic maps and hence share the new faster rate of convergence results within their corresponding FLAG.