Emotion plays an important role in human cognition and performance. Motivated by this, we investigate whether analogous emotional signals can shape the behavior of large language models (LLMs) and agents. Existing emotion-aware studies mainly treat emotion as a surface-level style factor or a perception target, overlooking its mechanistic role in task processing. To address this limitation, we propose E-STEER, an interpretable emotion steering framework that enables direct representation-level intervention in LLMs and agents. It embeds emotion as a structured, controllable variable in hidden states, and with it, we examine the impact of emotion on objective reasoning, subjective generation, safety, and multi-step agent behaviors. The results reveal non-monotonic emotion-behavior relations consistent with established psychological theories, and show that specific emotions not only enhance LLM capability but also improve safety, and systematically shape multi-step agent behaviors.