One critical issue in steady-state and high-performance operation in future tokamak fusion reactors is to develop H-mode operational regimes that mitigate or eliminate the large-amplitude ELMs to decrease the transient heat flux on the divertor and first wall. This paper reviews recent advances in extending and understanding the access and sustainment of natural and impurity-induced small/no-ELM H-mode regimes in EAST. Highly reproducible stationary grassy ELM regime with good energy confinement and excellent tungsten impurity exhaust capability has been obtained in EAST with water-cooled metal wall, compatible with low rotation, high normalized density, high bootstrap current fraction, radiative divertor and fully non-inductive operations, which are the conditions required for future fusion reactor-level plasmas. Grassy-like small-ELM H-mode regime has been achieved in helium (He) plasma experiments, which will be conducted during the pre-fusion power operation phase in ITER. The exploration for type-II ELM regime in EAST is also briefly introduced. Three spontaneous no-ELM H-mode regimes frequently observed in EAST are introduced, including an enhanced-recycling no-ELM regime, a non-inductive low-recycling no-ELM regime and a transient spontaneous no-ELM regime at relatively low pedestal collisionality ($${v}_{e}^{*}<1$$
v
e
∗
<
1
). These no-ELM regimes show different characteristic signatures of pedestal fluctuation and profiles, and the physical mechanisms behind have been studied. In addition, small/no-ELM regimes with impurity seeding have also been achieved in EAST. The ELM behavior changing from mixed small and large ELMs to pure grassy ELMs has been observed with neon (Ne) seeding. A highly reproducible no-ELM H-mode regime with radiative divertor has been demonstrated through CD4 seeding in EAST. These results are believed to be helpful for the application of small/no-ELM H-mode regimes to future tokamak fusion reactors.