Compelling visual effects and immersive virtual environments demand realistic material models that describe how light interacts with them. Important appearance effects are missing in conventional material models due to the built-in ray optics assumption. For example, rendered backlit hair is much dimmer than it is in real life and colorful glints are missing in dark animal fur. To improve the realism of visual effects and VR/AR applications, advanced material models that consider the wave nature of light are essential. This dissertation includes two wave based fiber scattering models for rendering human hair, animal fur and cloth fibers, and another work that combines the simulation of fluid dynamics and wave optics to reproduce iridescent water droplets from a cup of hot tea. By qualitative comparisons to photographs, these works demonstrate the importance of integrating wave optics into rendering. In these works, we leverage different computational electromagnetics methods including the boundary element method (BEM), physical optics approximations, and analytic solutions, and make the wave scattering computation tractable. The new material models are integrated into a path tracer to render scenes at a large scale with wave phenomena. This thesis includes the first wave optics based fiber scattering model in computer graphics, introducing an azimuthal scattering function that comes from a full wave simulation. We assume fibers are extruded from arbitrary cross-sections so that we can solve for a 3D electromagnetic field in a 2D domain using the boundary element method (BEM) efficiently. Our results show color effects, softening of sharp features, and strong forward scattering that are not predicted by traditional ray-based models. In the second work, we improve on the ideal extrusion assumption assumed in the first work and include surface roughness and tilted cuticle scales on fibers, which are known to be important for the appearance of hair and fur. We present a model based on a physical optics approximation and handle fibers with an arbitrary 3D microgeometry. We simulate surface reflection and diffractive scattering, and reproduce visually important color glints on hair and fur that were missed by all previous models. We also model the appearance of iridescent water droplets, motivated by the color patterns and granular textures both on the water surface and in the steam coming from a cup of hot tea. Iridescence on the water surface is caused by droplets levitating above the surface, and interference between light scattered by drops and reflected by the water surface, known as Quetelet scattering, is essential to producing the color. We propose a model, new to computer graphics, for rendering this phenomenon. For iridescent steam, we show that variation in droplet size is essential to the characteristic color patterns. We build a droplet growth model and apply it as a post-processing step to an existing computer graphics fluid simulation to compute collections of particles for rendering. Our model reproduces color patterns correlated with the steam flow, similar to the captures. This dissertation contributes to bridging computational electromagnetic studies and rendering research via the aforementioned new material models. There are exciting future directions in applying these techniques to develop other wave based materials models, modeling structural coloration in biology, and potentially leveraging wave optics for inverse design problems.