Specifically focusing on the landscape of abstractive text summarization, as opposed to extractive techniques, this survey presents a comprehensive overview, delving into state-of-the-art techniques, prevailing challenges, and prospective research directions. We categorize the techniques into traditional sequence-to-sequence models, pre-trained large language models, reinforcement learning, hierarchical methods, and multi-modal summarization. Unlike prior works that did not examine complexities, scalability and comparisons of techniques in detail, this review takes a comprehensive approach encompassing state-of-the-art methods, challenges, solutions, comparisons, limitations and charts out future improvements - providing researchers an extensive overview to advance abstractive summarization research. We provide vital comparison tables across techniques categorized - offering insights into model complexity, scalability and appropriate applications. The paper highlights challenges such as inadequate meaning representation, factual consistency, controllable text summarization, cross-lingual summarization, and evaluation metrics, among others. Solutions leveraging knowledge incorporation and other innovative strategies are proposed to address these challenges. The paper concludes by highlighting emerging research areas like factual inconsistency, domain-specific, cross-lingual, multilingual, and long-document summarization, as well as handling noisy data. Our objective is to provide researchers and practitioners with a structured overview of the domain, enabling them to better understand the current landscape and identify potential areas for further research and improvement.