Cross-lingual transfer in NLP is often hindered by the ``script barrier'' where differences in writing systems inhibit transfer learning between languages. Transliteration, the process of converting the script, has emerged as a powerful technique to bridge this gap by increasing lexical overlap. This paper provides a comprehensive survey of the application of transliteration in cross-lingual NLP. We present a taxonomy of key motivations to utilize transliterations in language models, and provide an overview of different approaches of incorporating transliterations as input. We analyze the evolution and effectiveness of these methods, discussing the critical trade-offs involved, and contextualize their need in modern LLMs. The review explores various settings that show how transliteration is beneficial, including handling code-mixed text, leveraging language family relatedness, and pragmatic gains in inference efficiency. Based on this analysis, we provide concrete recommendations for researchers on selecting and implementing the most appropriate transliteration strategy based on their specific language, task, and resource constraints.