Evolutionary histories, or phylogenies, play a central role in almost all of biology. They help explain how species evolved and diversified and how traits arose and spread. Further, they provide an interpretive framework for biological systems. For example, they help understand how genomes expand and shrink, how their contents rearrange, and how properties of biological systems emerge. Therefore, it is very important to infer evolutionary histories with high accuracy and efficiency. The post-genomic era has provided the data that is very promising for accurate inference. However, along with promise come modeling issues that must be resolved to enable inference. In this talk, I will discuss a process referred to as incomplete lineage sorting, or ILS, discuss how it results in complex patterns of evolutionary histories, and how to model it mathematically. I will then describe novel algorithms for inference under these models.