The realization of a successful monetary union among EAC partner states depends upon a sufficient degree of convergence of partners economies to established criteria. Gathering but scattered research has begun assessing the various benchmarks for this characteristic. This work integrates and synthesizes the various findings of literature with the view of providing a general perspective on how far the partner states have reached in meeting the macroeconomic convergence criteria and whether they have met the precondition for ascending the union. The review is done with anticipation of uncovering the challenges countries are encountering in aligning the economies to set criteria and what possible policy strategies exist to overcome these problems. Findings reveal that there has been very limited convergence. Generally countries remain behind the staged indictors. Progress to the monetary union is challenged by the highly demanding criteria, lack of exchange rate mechanism, obstacles to the common market, multiple memberships and many more. While countries might have the option of revising the benchmarks, efforts to strengthen national economic growth, build regional capacities, harmonize policies related to the monetary union, and correct constraints in the common market will enhance deeper integration and contribute greatly to macro-economic convergence.