The periocular region as a biometric trait has recently gained considerable traction, especially under challenging scenarios where reliable iris information is not available for human authentication. In this paper, we consider the problem of one-to-one (1 : 1) matching of highly nonideal periocular images captured in-the-wild under unconstrained imaging conditions. Such images exhibit considerable appearance variations, including nonuniform illumination variations, motion and defocus blur, off-axis gaze, and nonstationary pattern deformations. To address these challenges, we propose periocular probabilistic deformation models (PPDMs) that: 1) reduce the image matching problem to matching local image regions and 2) approximate the periocular distortions by local patch level spatial translations whose relationships are modeled by a Gaussian Markov random field. Given a periocular image pair, we determine the distortion-tolerant similarity metric by regularizing local match scores by the maximum aposteriori probability estimate of the relative local deformations between them. Unlike the existing global periocular image matching techniques, by accounting for local image deformations in the periocular matching process, PPDM exhibits greater tolerance to pattern variations. We demonstrate the effectiveness of our model via extensive evaluation on a large number of in-the-wild periocular images. We find that PPDMs outperform many benchmark 1 : 1 image matching techniques (improving verification rates at 0.1% false accept rate by ~30% over previous work and ~40% when compared with the best baseline) in challenging scenarios leading to state-of-the-art verification performance on multiple real-world periocular data sets.