By a theorem of Eliashberg, two overtwisted contact structures on a 3-manifold which belong to the same homotopy class (as plane fields), are also isotopic (through contact structures). Is there an example known of two non-isotopic but homotopic tight contact structures on a contact 3-manifold? 



non-isotopic but homotopic tight contact structure
Yes, there are known examples. See for example Corollary 1.3C of [this paper](http://resolver.sub.uni-goettingen.de/purl?GDZPPN002069210) of Eliashberg and Polterovich for an infinite sequence of examples on $T^3$. There is also a short paper of [Akbulut and Matveyev](http://msp.org/pjm/1998/182-2/p01.xhtml) giving examples on homology spheres. There may also be other examples known from the classification results of Giroux and Honda. 


