Deconstruction is the most prominent example of the post-structuralist criticisms, which both use and critique structuralism.
Deconstruction focuses on the displacements and gaps in the meaning structures generated by structuralism, which structuralists dismiss as exceptions. In other words, every text includes irreconcilable differences in meaning, and is therefore essentially meaningless--which is why people hate Deconstruction so much.
Associate the following terms and people with Deconstruction:
-erasure, trace, bracketing, differance, slippage, dissemination, logocentrism, indeterminacy, decentering
-(Structuralism) mimesis, alterity, marginality, desire, lack
-Jacques Derrida
For more information, I recommend Culler's Literary Theory: A Very Short Introduction.