What do exotic equations of state have to offer?

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 meeting. It is demonstrated that exotic equations of state are {\it not} soft if the vacuum contributions are large enough, and argued that recent measurements of high pulsar masses ($M \geq 2 M_{\odot}$) create problems for {\it hadronic} models in which hyperons should be present.