Chemotaxis, the directed movement of cells or living organisms in response to the concentration gradient of chemical substances, plays a significant role in a large range of biological phenomena such as tumor growth, wound healing, and embryo development. In this talk, first, we will introduce the chemotaxis model. Then, we will talk about the stability and instability of the constant solution. Next, we will discuss the local and global bifurcation and spiky stationary solutions which can be used to model cell aggregation. Finally, we will present some numerical simulations that illustrate our theoretical results and demonstrate some fascinating cellular aggregation phenomena.