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Acoustic metamateiral (AM) is an artificially structured material with the unique properties that cannot be found in nature materials, such as negative refraction, slab focusing, super-resolution imaging, cloaking, inverse Doppler effect, etc. In this paper we first review the research advances in AM in recent 20 years and then mainly discuss the properties of the meta-atom AM (MAAM), meta-molecule AM (MMAM), meta-atom cluster AM, and meta-molecule cluster AM. The MAAM consists of local resonant meta-atoms, whose resonant frequency is related to the geometry size of the structure. The MAAM presents the transmission dip and inversed phase near the resonant frequency. The meta-atoms discussed in the paper contain the split hollow sphere and hollow tube (HT), which can be used to realize the AM with single negative modulus and AM with single negative mass density near the frequency, respectively. The effective parameter of the MAAM is calculated from the transmission and reflection data in experiment according to the homogeneous-medium theory. By combining the two kinds of meta-atoms together, the assembled two-layered composite AM presents a transmission peak similar to the electromagnetic metamaterial in the overlapping resonant frequency region. The effective parameters calculated by experimental data demonstrate that the composite AM could realize simultaneously negative modulus and negative mass density near the peak frequency. In the double-negative band, this kind of double-negative AM can faithfully distinguish the acoustic sub-wavelength details (/7). Furthermore, by coupling the two kinds of meta-atoms in a structure, we design a flute-like meta-molecule structure of perforated hollow tube, which can be used to fabricate double-negative AM in high or low frequency band. The experimental results also show that the double-negative AM has the properties of flat focusing and negative refraction effect. Based on the weak interaction of the meta-atoms, the meta-atom cluster AM can be fabricated by arraying different sized meta-atoms. The meta-atom cluster AM composed of different sized meta-atoms of SHSs can realize multi-band or broadband negative modulus, and the different sized meta-atoms of HTs can realize broadband negative mass density. Similarly, the meta-molecule cluster AMs are constructed with seven kinds of flute-like perforated hollow tubes, which can overcome the limitations of arbitrary broadband negative bulk modulus and mass density to provide a region of inverse Doppler effects. It is also shown that the inverse frequency shift values will be enhanced with the increase of frequency. As the resonant unit can realize the effect of discontinuous phase, it can be used to design acoustic metasurface (AMS) to control the acoustic wavefronts at will and realize the anomalous manipulation of acoustic waves. Finally, we introduce the research status and tendency of AMS in coming years.