The capabilities of artificial intelligence systems have been advancing to a great extent, but these systems still struggle with failure modes, vulnerabilities, and biases. In this paper, we study the current state of the field, and present promising insights and perspectives regarding concerns that challenge the trustworthiness of AI models. In particular, this paper investigates the issues regarding three thrusts: safety, privacy, and bias, which hurt models' trustworthiness. For safety, we discuss safety alignment in the context of large language models, preventing them from generating toxic or harmful content. For bias, we focus on spurious biases that can mislead a network. Lastly, for privacy, we cover membership inference attacks in deep neural networks. The discussions addressed in this paper reflect our own experiments and observations.