The advent of 3D printing brings about the possibilities of lattice structures as advanced and novel sound absorbers. Lattice structures are defined as periodic cellular solids with submillimeter-sized features (such as struts, shells, or plates) spatially arranged in a three-dimensional manner. Advantages of lattice structures over traditional sound absorbers include them being fully designable, customizable, and with the potential for multifunctionalities. Herein, we present our results on the design, sound absorption properties, mechanisms, and multifunctional properties of several types of lattice structures that we have proposed. The first study focuses on metallic face-centred cubic based plate and truss structures. Measurements reveal that all of the lattice structures display absorption curves with characteristic resonance peaks. Sound absorption mechanisms of the lattice structures are proposed to be based on the multilayered Helmholtz resonator principle and analytical models are derived. Absorption coefficients are found to be essentially determined by the pore and cavity geometries. Following this, we have next leveraged the analytical model for the design and optimization of heterogeneous lattice structure absorbers. The heterogeneous structures thus present much improved absorption bandwidths. Numerical methods reveal the broadband capabilities to be based on multiple resonance modes working in tandem. Finally, we have also proposed a new type of hollow lattice that harness dual sound dissipation mechanisms. Enhanced broadband absorption can be achieved at specific geometries. For all of the cases, the lattice structures also dual function as energy absorbers under compressive impact. High specific strengths and energy absorptions are revealed for the metallic lattices, whilst polymeric ones display high deformation recoverability and tolerance. Overall, we present a new concept on the specific structural design and materials selection for lattice structures with simultaneously excellent sound absorption and mechanical properties.