The glass transition involves more than one dynamic relaxation mechanisms in supercooled liquids, such as α relaxation, slow β relaxation and fast β relaxation and so on. For the traditional theoretical system, α relaxation is believed mainly responsible for the nature of the glass transition as the beginning of the phenomenon. This idea, however, has been open to a big challenge since recent studies have indicated that slow β relaxation closely relates to α relaxation. Slow β relaxation determines the characteristics of α relaxation and is the precursor and the more microscopic base of glass transition behavior. In order to illuminate the significance of slow β relaxation in the fields of the glass transition and the structure of supercooled liquids, the accomplished progress is summarized from different aspects such as on the correlation between α relaxation and slow β relaxation, on the manner of α-slow β relaxation merging, on the energy landscape, on the excess wing and on the thermodynamically phenomenological models. The tendency of investigation in slow β relaxation is also evaluated. glass transition, β relaxation, liquid fragility, energy landscape, excess wing, boson peak Citation: Hu L N, Zhang C Z, Yue Y Z, et al. A new threshold of uncovering the nature of glass transition: The slow β relaxation in glassy states.The nature of glass transition is one of the most focal and difficult points in the field of condensed matter physics, because the glass transition of complicated dynamic heterogeneity involves a dramatic slowing down of the structural relaxation, which ultimately brings the supercooled liquid into the glassy state. Correspondingly, the relaxation dynamics of supercooled liquids evolves with time from atomic vibrations, motion of cages, the β (secondary) relaxation, to finally the onset of fully cooperative α (primary) relaxation process [1]. In different methods of measurements, the relaxations with different mechanisms generally have different performance. Figure 1 gives the schematic view of the frequency-dependent dielectric loss in nonconducting glass-forming materials at constant temperatures. It is seen that the α relaxation peak at the lowest region of frequency is followed by another peak at a relatively high frequency range, which is attributed to the β relaxation. According to the classic theory of glass transition, the cooperative α relaxation which occurs in the long or medium range is believed mainly responsible for the glass transition phenomenon, whereas the β relaxations that occur at shorter times or higher frequencies play no important role; the α relaxation is the base of the glass transition. Based on this idea, a lot of theories (mainly from aspects of free volume [2] and the configurational entropy [3]) have been proposed, resulting in a general classical physicochemical picture of dynamic structural relaxation and thermodynamic glass transition. This idea, however, has been open to a big challenge since β relaxations, especially Johari-Goldstein type in rigid molecule...