Due to the unique crystal structures and excellent transport properties, the Zintl phase thermoelectric materials have aroused extensive interest in energy storage and conversion. To explore the origins of those excellent performances, a series of experimental and theoretical techniques have been applied, such as neutron scattering, thermal conductivity, and molecular dynamics simulations with machine learning. In this paper, the progress of neutron scattering research on the structure and dynamics of Zintl phase is summarized, for example A₁₄MPn₁₁ compounds with zero-dimensional (0D) substructures, 1D chains-based compounds, 2D layered A₂BX₂ compounds (including the binary Mg₃Sb₂) and their structural variants, as well as AB₄X₃, and ZrBeSi-type compounds. The underlying mechanisms of intrinsically low lattice thermal conductivity in those Zintl phase are discussed in detail. These compounds generally exhibit the following characteristics: 1) strong anharmonicity, which is characterized by strong atomic vibrations and anharmonic phonon-phonon scattering; 2) weak chemical bonding, which usually leads to low sound velocity and interatomic force constants, and corresponding to low-energy phonon branches; 3) intrinsic vacancy defect, which weakens the bond strengths, softens the lattice, and enhances anharmonic phonon-phonon scattering. Neutron diffraction is applied to studying crystal structures, lattice parameters, atomic occupancies, and atomic displacement parameters. Inelastic neutron scattering measures the lattice dynamics, and density of states, which are related to lattice thermal conductivity. Hence, the physical mechanisms of Zintl compounds are analyzed for optimizing material properties and designing new functional materials.