I would like to organize a seminar on crystalline cohomology; I dream of understanding the Beilinson's recent paper on the mysterious functor (http://www.ams.org/journals/jams/2012-25-03/S0894-0347-2012-00729-2/S0894-0347-2012-00729-2.pdf). Yet the content of the seminar is not fixed at the moment, and the participants don't know much on the subject. So, I would like to have some choice of readable texts on related matters, and I would like to impress the participants with some impressive results of this theory.
My last attempt to study crystalline cohomology was almost 10 years ago, and I am not sure that I have got the correct picture of the subject then. Yet I remember that there are several alternatives to crystalline cohomology (including rigid cohomology and Monsky-Washnitzer one). Which of the versions is the most 'interesting' and 'important'; which statements of the subject are the most important (and could be undersood by a non-expert)? Any comments and references would be very welcome! I would prefer to avoid modularity questions.