The Lambda-Cold dark matter paradigm have been a successful working theory to explain most of our current observations of the cosmos. When this paradigm is used to explain the late universe, we usually include a simple assumption that galaxies live in halos, and that bigger galaxies live in bigger halos. This assumption is mostly consistent with our observation, and is backed up by hydrodynamical simulations. It has also shed light on our understandings of galaxy formation and evolution. On the other hand, it has now become clear that this simple, zeroth-order galaxy-halo connection is not the end of the story. The assembly history of halos affects the galaxies reside in, and also affects the clustering properties of halos. This effect, usually known as “assembly bias,” has brought new challenges to our ability to accurately model the galaxy-halo connection. A class of galaxy-halo connection models that take assembly bias into account has emerged, but it at the same time highlights the complex nature of assembly bias. In this talk I will discuss a few different aspects of assembly bias, focusing on how it affects the galaxy-halo connection and also its implications.