Coherence describes the validity of the internal rules that drive the behaviors of a virtual environment (VE) in presenting a credible scenario. A VR system with a high level of coherence could lead to strong plausibility illusion, which is a key component of the sense of presence. There are few existing studies centered around coherence, and they tend to put the user in a passive role when experiencing the VE without emphasizing on their active participation in the interaction. This dissertation makes up this gap by connecting the concept of coherence with fundamental 3D user interface design that focuses on the algorithms that map the user's actions to the VE's behaviors. Specifically, we inspect the design of coherent interactions for two complicated tasks, namely travel and object manipulation. For travel, we propose a family of redirected walking techniques called "narrative driven cell-based redirection", which lets the user traverse a VE that's much larger than the physical space without breaking the coherence of the scenario. For object manipulation, we propose the novel concept of physics coherence to capture whether an interface conforms to the rules of physics and design several novel techniques that try to balance between physics coherence and usability. Together, we provide some useful tools for designing coherent interactions and discuss how coherence affects user experience in VR interaction.