  We study the compactness and the hypercyclicity of Toeplitz operators in the
de Branges-Rovnyak spaces H(b) with co-analytic and bounded symbols on D. We
highlight the fundamental role played by the function b generating the de
Branges-Rovnyak space H(b). The characterization of compactness depends wether
b is inner function or not and the characterization of hypercyclicity depends
wether the function log(1-|b|) is integrable or not.
