The Coalgebraic Logic seminar took place between the 6th and 9th of December 2009 at the Leibniz Forschungszentrum Schloss Dagstuhl. The event was very well received, with more than 35 scientists from Europe, the United States, Canada and China attending, and with more than thirty presentations during the three days. Given the unforeseen enthusiasm of the meeting's reception, we thought that it would be a good idea for us to put together a special journal issue dedicated to this topic. We were also encouraged by the positive response we received from Guiseppe Longo, who indicated his interest in a special issue for Mathematical Structures in Computer Science, and here we are.