We argued that immune system is an adaptive complex system. It is shown that it has emergent properties. Its network structure is of the small world network type. The network is of the threshold type, which helps in avoiding autoimmunity. It has the property that every antigen (e.g. virus or bacteria) is typically attacked by more than one effector. This stabilizes the equilibrium state. Modelling complex systems is discussed. Cellular automata (CA)-type models are successful, but there are much less analytic results about CA than about other less successful models e.g. partial differential equations (PDE). A compromise is proposed.