Abstract: Seismic impedance inversion is one of the key research subjects in the field of seismic exploration. Its basic goal is to quantitatively predict the wave impedance of underground medium from the seismic data. In recent years, with the rapid advancement of artificial intelligence technology, many scholars have proposed a variety of deep leaning (DL) based seismic impedance inversion methods. These methods embed geophysical information, such as physical laws, empirical formulas, and prior expert knowledge, into deep networks from different perspectives, effectively reducing the multi-solution and enhancing the physical interpretability of the inversion problem. This paper presents a review of these methods, which incorporate geophysical information by three strategies: ① designing network architectures embedded with geophysical knowledge; ② applying data constraints; ③ constructing multi-objective loss functions. The network architectures embedded with geophysical knowledge include: a forward physical model module, a reflection coefficient inversion model module, a seismic data spatiotemporal feature representation module, and a synthetic-to-real domain adaptation module. Data constraints include: generating diverse synthetic samples to train the deep network, and quantifying prior knowledge as inputs to the network. Multi-objective loss functions encompass physics-informed regularization terms, including closed-loop loss, generative adversarial loss, dynamic time warping (DTW) loss, spatial structure loss, and uncertainty loss. These strategies can reduce the multi-solution and enhance the reliability of the inversion problem from different perspectives. Finally, this paper provides two prospects for the DL-based seismic impedance inversion method: ① multi-modal large models with robust comprehension and knowledge reasoning capabilities can be leveraged together with multi-modal data to enhance the generalization of the inversion model; ② the multi-model fitting method can be combined with physics-informed neural network (PINN) to transform the "one-to-many" problem of inversion modeling into a "one-to-one" problem within each seismic facies segment, thereby reducing the multi-solution of the seismic impedance inversion.