Reliable health assessment of retired lithium-ion batteries is essential for safe and economically viable second-life deployment, yet remains difficult due to sparse measurements, incomplete historical records, heterogeneous chemistries, and limited or noisy battery health labels. Conventional laboratory diagnostics, such as full charge-discharge cycling, pulse tests, Electrochemical Impedance Spectroscopy (EIS) measurements, and thermal characterization, provide accurate degradation information but are too time-consuming, equipment-intensive, or condition-sensitive to be applied at scale during retirement-stage sorting, leaving real-world datasets fragmented and inconsistent. This review synthesizes recent advances that address these constraints through physical health indicators, experiment testing methods, data-generation and augmentation techniques, and a spectrum of learning-based modeling routes spanning supervised, semi-supervised, weakly supervised, and unsupervised paradigms. We highlight how minimal-test features, synthetic data, domain-invariant representations, and uncertainty-aware prediction enable robust inference under limited or approximate labels and across mixed chemistries and operating histories. A comparative evaluation further reveals trade-offs in accuracy, interpretability, scalability, and computational burden. Looking forward, progress toward physically constrained generative models, cross-chemistry generalization, calibrated uncertainty estimation, and standardized benchmarks will be crucial for building reliable, scalable, and deployment-ready health prediction tools tailored to the realities of retired-battery applications.