Ever since 1911, the Solvay Conferences have shaped modern physics. The format is quite different from other conferences as the emphasis is placed on discussion. The 26th edition held in October 2014 in Brussels and chaired by Roger Blandford continued this tradition and addressed some of the most pressing open questions in the fields of astrophysics and cosmology, gathering many of the leading figures working on a wide variety of profound problems.The proceedings contain the 'rapporteur talks' giving a broad overview with unique insights by distinguished renowned scientists. These lectures cover the five sessions: 'Neutron Stars', 'Black Holes', 'Cosmic Dawn', 'Dark Matter' and 'Cosmic Microwave Background'.In the Solvay tradition, the proceedings also include the prepared comments to the rapporteur talks. The discussions among the participants -- expert, yet lively and sometimes contentious -- have been edited to retain to retain their flavor and are reproduced in full. The reader is taken on a breathtaking ride through 42 years of extraordinary discovery since astrophysics was last on the Solvay program and 57 years since cosmology was last discussed.