Automatic spoken language identification (LID) is a very important research field in the era of multilingual voice-command-based human-computer interaction (HCI). A front-end LID module helps to improve the performance of many speech-based applications in the multilingual scenario. India is a populous country with diverse cultures and languages. The majority of the Indian population needs to use their respective native languages for verbal interaction with machines. Therefore, the development of efficient Indian spoken language recognition systems is useful for adapting smart technologies in every section of Indian society. The field of Indian LID has started gaining momentum in the last two decades, mainly due to the development of several standard multilingual speech corpora for the Indian languages. Even though significant research progress has already been made in this field, to the best of our knowledge, there are not many attempts to analytically review them collectively. In this work, we have conducted one of the very first attempts to present a comprehensive review of the Indian spoken language recognition research field. In-depth analysis has been presented to emphasize the unique challenges of low-resource and mutual influences for developing LID systems in the Indian contexts. Several essential aspects of the Indian LID research, such as the detailed description of the available speech corpora, the major research contributions, including the earlier attempts based on statistical modeling to the recent approaches based on different neural network architectures, and the future research trends are discussed. This review work will help assess the state of the present Indian LID research by any active researcher or any research enthusiasts from related fields.