Large language models (LLMs) have exploded a new heatwave of AI for their ability to engage end-users in human-level conversations with detailed and articulate answers across many knowledge domains. In response to their fast adoption in many industrial applications, this survey concerns their safety and trustworthiness. First, we review known vulnerabilities and limitations of the LLMs, categorising them into inherent issues, attacks, and unintended bugs. Then, we consider if and how the Verification and Validation (V&V) techniques, which have been widely developed for traditional software and deep learning models such as convolutional neural networks as independent processes to check the alignment of their implementations against the specifications, can be integrated and further extended throughout the lifecycle of the LLMs to provide rigorous analysis to the safety and trustworthiness of LLMs and their applications. Specifically, we consider four complementary techniques: falsification and evaluation, verification, runtime monitoring, and regulations and ethical use. In total, 370+ references are considered to support the quick understanding of the safety and trustworthiness issues from the perspective of V&V. While intensive research has been conducted to identify the safety and trustworthiness issues, rigorous yet practical methods are called for to ensure the alignment of LLMs with safety and trustworthiness requirements.