Speech-to-text translation pertains to the task of converting speech signals in a language to text in another language. It finds its application in various domains, such as hands-free communication, dictation, video lecture transcription, and translation, to name a few. Automatic Speech Recognition (ASR), as well as Machine Translation(MT) models, play crucial roles in traditional ST translation, enabling the conversion of spoken language in its original form to written text and facilitating seamless cross-lingual communication. ASR recognizes spoken words, while MT translates the transcribed text into the target language. Such disintegrated models suffer from cascaded error propagation and high resource and training costs. As a result, researchers have been exploring end-to-end (E2E) models for ST translation. However, to our knowledge, there is no comprehensive review of existing works on E2E ST. The present survey, therefore, discusses the work in this direction. Our attempt has been to provide a comprehensive review of models employed, metrics, and datasets used for ST tasks, providing challenges and future research direction with new insights. We believe this review will be helpful to researchers working on various applications of ST models.