<p>Optical interferometry is a cornerstone technique in precision metrology that enables non-contact measurement of surface and wavefront geometries with nanometer-level sensitivity. Since the geometrical characteristics of measured samples are encoded as phase distributions, accurate phase measurements have been a central research topic over the past decades. However, traditional phase retrieval methods suffer from environmental disturbances, accumulated nonlinearities, and limited robustness in real industrial environments. Recent advances in deep learning have introduced new possibilities for accurate and fast phase measurements, enabling single- or few-shot reconstructions that were previously infeasible. This review aims to provide a clear and organized overview of deep learning-based phase measurements in optical interferometry. First, the principles of interferometric imaging and conventional retrieval techniques are summarized. We then describe training data preparation approaches, including experimental, synthetic, and hybrid methods, highlighting their strengths and limitations. Deep learning-based phase measurement methods are classified into three major categories, providing an intuitive framework for understanding different network architectures and inference strategies. Finally, we discuss the remaining challenges that limit the industrial deployment of deep learning-based methods, including domain gaps, unreliable ground truth, black-box behavior of the network, and lack of large-scale repeatability testing. Emerging solutions such as domain adaptation, digital-twin simulation, and physics-informed neural networks have been introduced as promising approaches.</p>