Quantum information processing rests on our ability to manipulate quantum s
uperpositions through coherent unitary transformations, and to establish en
tanglement between constituent quantum components of the processor. The qua
ntum information processor (a linear ion trap, or a cavity confining the ra
diation field for example) exists in a dissipative environment. We discuss
ways in which entanglement can be established within such dissipative envir
onments. We can even make use of a strong interaction of the system with it
s environment to produce entanglement in a controlled way.