The paper provides a critical assessment on the environmental efficiency of economic growth, from a methodological perspective. The general framework for the decoupling analysis is first presented, with a specific focus on waste resource indicators. Current experiences of de-linking analysis are discussed and commented. The environmental Kuznets curves arena is then addressed as a natural extension of any analysis on the environmental efficiency of economic growth. Some critical issues and research suggestions are discussed. We finally provide preliminary empirical evidence on environmental Kuznets curve for waste indicators using a European countries dataset. Empirical evidence on packaging and municipal waste shows that decoupling seems to occur only on a relative basis. No significant evidence on an inverted U-shape is found for both waste indicators. Europe appears still lagging behind in reaching the critical turning point concerning the relationship between waste and consumption indicators. The lack of explicit targets referring to waste prevention at source, in addition to recovery/reuse/recycling goals, may be the primary reason behind the absence of a strong Delinking process in the case of primary waste sources. The applied panel investigation, though informative since it is focussed on a homogenous Regional area, indicates the need of further work, exploring the occurrence of delinking processes relatively to specific materials and/or focussing on specific countries.