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Synthetic aperture radar (SAR) interferometry has rapidly evolved in the last decade and can be considered today as a mature technology, which incorporates computationally intensive and data-intensive tasks. In this paper, a perspective on the state-of-the-art of high performance computing (HPC) methodologies applied to spaceborne SAR interferometry (InSAR) is presented, and the different parallel algorithms for interferometric processing of SAR data are critically discussed at different levels. Emphasis is placed on the key processing steps, which typically occur in the interferometric techniques, categorized according to their computational relevance. Existing implementations of the different InSAR stages using diverse parallel strategies and architectures are examined and their performance discussed. Furthermore, some InSAR computational schemes selected in the literature are analyzed at the level of the entire processing chain, thus emphasizing their potentialities and limitations. Therefore, the survey focuses on the inherent computational approaches enabling large-scale interferometric SAR processing, thus offering insight into some open issues, and outlining future trends in the field.