Over the past two decades, acoustic metamaterials have emerged as a transformative technology for precise sound manipulation, offering sub-wavelength thickness, broad bandwidth, and tunable properties for applications in medical ultrasound, noise control, and nondestructive testing. To analyze their sound propagation characteristics and underlying mechanisms, this chapter introduces fundamental theoretical frameworks and modeling methods, including the interference theory, effective medium theory, finite element method, generalized Snell’s law, mode conversion theory, and band theory of sonic crystals. These theories provide essential methodological support for studying the effects of acoustic asymmetric transmission, acoustic focusing, and acoustic asymmetric focusing while elucidating the physical principles behind wave manipulation in two- and three-dimensional spaces.