Due to the unique crystal structures and excellent transport properties, the Zintl phase thermoelectric materials have attracted extensive interest in energy storage and conversion. To explore the origins of those excellent performances, a series of experimental and theoretical techqiues have been applied, such as neutron scattering, thermal conductivity, molecular dynamics simulations with machine learning. In this review, the progress related to neutron scattering studies on the structure and dynamics of Zintl phase is summarized, for example <i>A</i><sub>14</sub><i>MPn</i><sub>11</sub> compounds with zero-dimensional (0D) substructures, 1D chains-based compounds, 2D layered <i>A</i><sub>2</sub><i>BX</i><sub>2</sub> compounds (including the binary Mg<sub>3</sub>Sb<sub>2</sub>) and their structural variants, as well as <i>AB</i><sub>4</sub><i>X</i><sub>3</sub>, 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 the study crystal structures, lattice parameters, atomic occupancies, and atomic displacement parameters. Inelastic neutron scattering measures the lattice dynamics and density-of-state, 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.