Large Language Models (LLMs) have been transformative across many domains. However, hallucination -- confidently outputting incorrect information -- remains one of the leading challenges for LLMs. This raises the question of how to accurately assess and quantify the uncertainty of LLMs. Extensive literature on traditional models has explored Uncertainty Quantification (UQ) to measure uncertainty and employed calibration techniques to address the misalignment between uncertainty and accuracy. While some of these methods have been adapted for LLMs, the literature lacks an in-depth analysis of their effectiveness and does not offer a comprehensive benchmark to enable insightful comparison among existing solutions. In this work, we fill this gap via a systematic survey of representative prior works on UQ and calibration for LLMs and introduce a rigorous benchmark. Using two widely used reliability datasets, we empirically evaluate six related methods, which justify the significant findings of our review. Finally, we provide outlooks for key future directions and outline open challenges. To the best of our knowledge, this survey is the first dedicated study to review the calibration methods and relevant metrics for LLMs.