Research on architected materials is advancing due to their potential in engineering applications. This study focuses on the development of metafilters for controlling elastic wave propagation, exploring their application in dispersive properties. Recent progress in additive manufacturing enables large-scale production of microstructured periodic lattices with acoustic properties. Chiral microstructures typical of phononic crystals create ideal band spectra for wave filtering, and local resonators open band gaps at low frequencies, making them metamaterials. By exploiting multiphysical coupling, band structures can be actively tuned to create metafilters or mechanical metadiodes for active (including non-reciprocal) control of wave propagation. Given the system complexity, continuum modeling is essential for capturing their static and dynamic properties. A high-fidelity continualization method is proposed to characterize dispersive behavior in the first Brillouin zone, leading to accurate models for wave propagation in active metamaterials with periodic microstructure.