Two types of limitations are discussed. The first ones are determined by specified requirements on acceptable complementary sensitivity and bounded gains in a fixed frequency region. Some necessary conditions for acceptable performance achieved by any decentralized control are shown. The second type appears due to decentralized uncontrollability/unobservability properties which imply the impossibility to move some eigenvalues by any decentralized feedback. If such eigenvalues are in the open right-hand side halfplane then the system is unstabilizable by such feedbacks. The statements are illustrated by some simple examples.