The quantum anomalous Hall (QAH) effect is a quantum Hall effect induced by spontaneous magnetization instead of an external magnetic field. The effect occurs in two-dimensional (2D) insulators with topologically nontrivial electronic band structure characterized by a non-zero Chern number. The experimental observation of the QAH effect in thin films of magnetically doped (Bi,Sb)2Te3 topological insulators (TIs) paves the way not only for practical applications of dissipationless quantum Hall edge states, but also for exploration of other novel quantum states of matter such as axion insulator, quantum spin Hall insulator, Weyl semimetal, and topological superconductor. In this talk, I will introduce our recent progresses on constructing and engineering heterostructures and multilayers based on magnetically doped (Bi,Sb)2Te3 QAH films. The QAH heterostructures and multilayers enable us to obtain and investigate various topological quantum states of matter and lay the foundation for studies on topological electronics and topological quantum computation.