Emergy accounting (EmA) is a method in the “sustainability assessment toolbox”, that has gained increasing interest due to several reasons: 1) it includes naturally economic flows alongside with energy and material flows (also other information flows than money can in theory be included but has yet not been done so to any larger extent); 2) EmA has interesting alternative solutions to problematic areas where the popular Ecological footprint method has gained criticism from the scientific community; 3) EmA as a complement to LCA may make it possible to develop the LCA method to assess also larger systems as cities, regions, and countries, which is not currently possible. There is currently no standard how EmA should be used in sustainability assessments. Preliminary features of a framework were presented at ISDRS 2016, and in this paper this framework is further developed and compared with ten recent emergy papers addressing sustainability. The ISDRS 2016 preliminary framework included 1) the Emergy Sustainability Index (ESI); 2) the normalizing mechanism in EmA; and 3) emergy as a network measure; in this paper is also included 4) pulsing sustainability. The results showed that all ten papers used the normalizing feature of energy, material and money. Eight of them included the possibility to capture network properties of the system investigated with indices and systems diagrams. Seven of them used the, to some extent disputed, Emergy Sustainability Index (ESI). None of the ten papers addressed the pulsing aspect of sustainability.