Abstract: Slow acoustic metamaterials are highly flexible systems for phase engineering applications. They have great potential in ultrathin acoustic devices, such as flat acoustic lenses,acoustic rectifiers, and self-accelerating beam generators. However, most slow acoustic metamaterials have serious dispersion and interface impedance mismatch and other problems. These defects restrict operation to a narrow bandwidth. To overcome this problem, novel helical-structured metamaterials may be used. We reviewed two helical-structures for implementing non-dispersive high effective refractive index slow acoustic devices and broadband impedance matching slow acoustic devices between two media with different impedances and cross section. We also provide some design guidelines, together with the basic principles. The performance characteristics of these devices may be tuned by varying the helicity of the structures. Finally, we demonstrate a self-accelerating beam on a prescribed parabolic trajectory using a one-dimension helical-structure metamaterial array with inhomogeneous cells.