Abstract: Planetary surfaces, shaped by billions of years of geologic evolution, display numerous impact craters whose distribution of size, density, and spatial arrangement reveals the celestial body's history. Identifying these craters is essential for planetary science and is currently mainly achieved with deep learning-driven detection algorithms. However, because impact crater characteristics are substantially affected by the geologic environment, surface materials, and atmospheric conditions, the performance of deep learning models can be inconsistent between celestial bodies. In this paper, we first examine how the surface characteristics of the Moon, Mars, and Earth, along with the differences in their impact crater features, affect model performance. Then, we compare crater detection across celestial bodies by analyzing enhanced convolutional neural networks and U-shaped Convolutional Neural Network-based models to highlight how geology, data, and model design affect accuracy and generalization. Finally, we address current deep learning challenges, suggest directions for model improvement, such as multimodal data fusion and cross-planet learning and list available impact crater databases. This review can provide necessary technical support for deep space exploration and planetary science, as well as new ideas and directions for future research on automatic detection of impact craters on celestial body surfaces and on planetary geology.