The literature on microgrid (MG) studies can be categorized as those that investigated the dynamics or economics of MG systems. Due to the important roles of battery energy storage systems (BESSs) in MGs, the BESSs have been involved in both economics and dynamics studies but mostly separately due to the different time constants of studies. Whereas, in the complicated modern MGs, the BESS is the joint point that bridges these two studies. Thus, studying merely one aspect of economy-dynamic without considering the other aspect would not be accurate. To bridge this gap, this paper reviews, analysis and classifies the BESSs applications, based on their time constants, by merging of which helps researchers to develop joint economy-dynamics models that would be the future trend in the field. The classified BESS applications are 1) inertia synthesis, 2) primary frequency response to compensate slow response time of micro-sources (MSs) for load tracking, 3) real-time energy management for the integration of intermittent renewables, 4) economic dispatch and optimal power flow for improving steady-state performance, and 5) slack bus realization. The research gaps and future trends have been discussed throughout the paper and are summarized in the future trend section.