Low frequency noise is a common problem in aircraft and launch vehicles. New technologies must be investigated to reduce this noise while contributing minimal weight to the structure. This thesis investigates passive and active control methods to improve low frequency sound absorption and transmission loss using acoustic metamaterials. The acoustic metamaterials investigated consist of poro-elastic acoustic heterogeneous (HG) metamaterials and microperforated (MPP) acoustic metamaterials. HG metamaterials consist of poro-elastic material with a periodic arrangement of embedded masses acting as an array of mass-spring- damper systems. MPP acoustic metamaterials consist of periodic layers of micro-porous panels embedded in poro-elastic material. This thesis examines analytically, experimentally, and numerically the behavior of acoustic metamaterials compared to a baseline poro-elastic sample. The development of numerical techniques using finite element analysis will aid in understanding the physics behind their functionality and will influence their design. Design studies are performed to understand the effects of varying the density, size, shape, and placement of the embedded masses as well as the location and distribution of microperforated panels in poro- elastic material. An active HG metamaterial is investigated, consisting of an array of active masses embedded within poro-elastic material. Successful tonal and broadband noise control is achieved using a feedforward, filtered-x LMS control algorithm to minimize the downstream sound pressure level. Low-frequency absorption and transmission loss is successfully increased in the critical frequency range below 500 Hz. Acoustic metamaterials are compact compared to conventional materials and find applications in controlling low-frequency sound radiation in aircraft and launch vehicles. / Master of Science