Parallel corpora play an important role in training machine translation (MT) models, particularly for low-resource languages where high-quality bilingual data is scarce. This review provides a comprehensive overview of available parallel corpora for Indic languages, which span diverse linguistic families, scripts, and regional variations. We categorize these corpora into text-to-text, code-switched, and various categories of multimodal datasets, highlighting their significance in the development of robust multilingual MT systems. Beyond resource enumeration, we critically examine the challenges faced in corpus creation, including linguistic diversity, script variation, data scarcity, and the prevalence of informal textual content.We also discuss and evaluate these corpora in various terms such as alignment quality and domain representativeness. Furthermore, we address open challenges such as data imbalance across Indic languages, the trade-off between quality and quantity, and the impact of noisy, informal, and dialectal data on MT performance. Finally, we outline future directions, including leveraging cross-lingual transfer learning, expanding multilingual datasets, and integrating multimodal resources to enhance translation quality. To the best of our knowledge, this paper presents the first comprehensive review of parallel corpora specifically tailored for low-resource Indic languages in the context of machine translation.