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Amorphous materials such as glass, polymer and amorphous alloy have broad applications ranging from daily life to extreme conditions due to their unique properties in elasticity, strength and electrical resistivity. A better understanding of atomic structure of amorphous materials will provide invaluable information for their further engineering and applications. However, experimentally determining the three-dimensional (3D) atomic structure of amorphous materials has been a long-standing problem. Due to the disordered atomic arrangement, amorphous materials do not have any translational and rotational symmetry at long-range scale. Conventional characterization methods, such as the scattering and the microscopy imaging, can only provide the statistic structural information which is averaged over the macroscopic region. The knowledge of the 3D atomic structure of amorphous materials is limited. Recently atomic resolution electron tomography (AET) has proven an increasingly powerful tool for atomic scale structural characterization without any crystalline assumptions, which opens a door to determine the 3D structure of various amorphous materials. In this review, we summarize the state-of-art characterization methods for the exploration of atomic structures of amorphous materials in the past few decades, including X-ray/neutron diffraction, nano-beam and angstrom-beam electron diffraction, fluctuation electron microscopy, high-resolution scanning/transmission electron microscopy, and atom probe tomography. From experimental data and theoretical descriptions, 3D structures of various amorphous materials have been built up. Particularly, we introduce the principles and recent progress of AET, and highlight the most recent groundbreaking feat accomplished by AET, i.e., the first experimental determination of all 3D atomic positions in a multi-component glass-forming alloy and the 3D atomic packing in amorphous solids. We also discuss the new opportunities and challenges for characterizing the chemical and structural defects in amorphous materials.