The human-like generative ability of Large Language Models (LLMs) has ushered in a new era of foundational models and generative AI, unlocking new possibilities and driving cross-domain innovations. However, the transformative potential of LLMs has been seriously challenged the problematic hallucinations of LLMs, which may lead to misinformation, biases, harmful content, making responsible finetuning of LLMs a grand challenge. Safety alignment of pretrained LLMs represents an important step forward to ensure their outputs being helpful, harmless, and honest, respecting human preferences and societal values. However, recent studies have shown that many safety-aligned LLMs suffer from security/privacy/ethic risks of user finetuning: the well-aligned LLMs can easily be broken and produce harmful, helpless or untruthful content in the presence of a small amount of harmful finetuning data. In this keynote, I will discuss some potential vulnerabilities and risks of existing safety alignment and finetuning techniques, and share some of our recent research efforts towards developing a responsible framework and techniques for more robust alignment/finetuning of LLMs.