Optical diffraction tomography (ODT) uses refractive index (RI) as endogenous dyes to non-invasively obtain three-dimensional (3D) structural information of biological samples, and is promising to achieve long-term dynamic observation for living samples (such as live cells, etc.), which is of great significance in the fields of biomedical and life sciences. However, ODT relies on weak scattering approximation and interferometric measurement. The former greatly limits the observation performance of this technology on thick samples such as clustered cells and tissues, and the latter significantly increases the complexity of the imaging system. To address these issues, researchers have developed a class of diffraction tomography based on the principle of non-interferometric intensity measurement. First, a basic description of non-interferometric intensity diffraction tomography (IDT) is provided, including its imaging system, imaging metrics, and reconstruction problem; Then, we introduce the research results and latest progresses of non-interferometric IDT from four technical routes: non-interferometric phase retrieval, 3D optical transfer function, multi-layer forward propagation model, and neural network, and compare the above methods; Finally, current problems and challenges as well as future research directions are discussed.