Amorphous materials have broad applications ranging from daily life to extreme conditions due to their unique properties in elasticity, strength and resistivity. However, experimentally determining the three-dimensional (3D) atomic structure of amorphous materials has been a long-standing problem. Atomic resolution electron tomography (AET) has proved an increasingly powerful tool for atomic scale structural characterization without any crystalline assumptions. 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. We introduce the principles and recent progresses of AET, and highlight the first groundbreaking experimental determination of all 3D atomic positions in amorphous solids. We also discuss the new opportunities and challenges for characterizing the chemical and structural defects in amorphous materials.