Bandpass filters with high frequency and wide bandwidth are indispensable parts of the fifth-generation telecommunication technologies, and currently, they are mainly based on surface and bulk acoustic wave resonators. Owing to its high mechanical strength, excellent stability at elevated temperatures, good thermal conductivity, and compatibility with complementary metal-oxide-semiconductor technology, aluminum nitride (AlN) becomes the primary piezoelectric material for high-frequency resonators. This review briefly introduces the structures and key performance parameters of the acoustic resonators. The common filter topologies are also discussed. In particular, research progresses in the piezoelectric AlN layer, electrodes, and substrates of the resonators are elaborated. Increasing the electromechanical coupling constant is the main concern for the AlN film. To synthesize AlN in single-crystalline or poly-crystalline with a high intensity of (0002) orientation, and alloy the AlN with other elements are two effective approaches. For the substrates and bottom electrodes, lattice and thermal expansion mismatch, and surface roughness are critical for the synthesis of a high-crystal-quality piezoelectric layer. The electrodes with low electrical resistance, large acoustic-impedance mismatch to the piezoelectric layer, and low density are ideal to reduce insertion loss. Based on the research progress, several possible research directions in the AlN-based filters are suggested at the end of the paper.