Pitting corrosion is a primary and most severe failure mechanism of oil and gas pipelines. To implement a prognostic and health management (PHM) for oil and gas pipelines corroded by internal pitting, an appropriate degradation model is required. An appropriate and highly reliable pitting corrosion degradation assessment model should consider, in addition to epistemic uncertainty, the temporal aspects, the spatial heterogeneity, and inspection errors. It should also take into account the two well-known characteristics of pitting corrosion growing behavior: depth and time dependency of pit growth rate. Analysis of these different levels of uncertainties in the amount of corrosion damage over time should be performed for continuous and failure-free operation of the pipelines. This paper reviews some of the leading probabilistic data-driven prediction models for PHM analysis for oil and gas pipelines corroded by internal pitting. These models categorized as random variable-based and stochastic process-based models are reviewed and the appropriateness of each category is discussed. Since stochastic process-based models are more versatile to predict the behavior of internal pitting corrosion in oil and gas pipelines, the capabilities of the two popular stochastic process-based models, Markov process-based and gamma process-based, are discussed in more detail.