We present a short general overview of the main features of exotic models of neutron stars, focusing on the structural and dynamical predictions derived from them. In particular, we discuss the presence of "normal" quark matter and Color-Flavor Locked (CFL) states, including their possible self-bound versions, and mention some different proposals emerging from the study of QCD microphysics. A connection with actual observed data is the main goal to be addressed at this talk and along the

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... . It is demonstrated that exotic equations of state are not soft if the vacuum contributions are large enough, and argued that recent measurements of high pulsar masses (M ≥ 2 M ⊙ ) create problems for hadronic models in which hyperons should be present.