This chapter, which has an introductory character, contains the main elements of the theory of block shift operators. These operators are among the simplest infinite dimensional operators, and they may serve as building blocks for more complicated operators. In the first section block forward shifts are identified as pure isometries. In the second section it is shown that block backward shifts provide universal models for arbitrary operators. The third section describes the invariant subspaces of ℂ m -block forward shifts. Throughout this chapter all operators are Hilbert space operators.