How do the brightest galaxies in the sky produce the vast amounts of energy that they are observed to radiate? Astronomers believe that this energy can be only produced in one of two ways: either by matter falling into a supermassive black hole at the center of the galaxy, or by star formation. Black holes are among the most enigmatic objects in the Universe. They represent the ultimate end-state of matter. In general, when an object's size decreases, the gravity at its surface increases. A black hole is formed when the gravity is so strong that not even light can escape its grasp. Black holes are known to have masses anywhere from a few times that of the Sun (stellar mass black holes, which are thought to be produced when a massive star explodes as a supernova), up to a mass of millions or even billions of times the Sun's mass (supermassive black holes). The latter are thought to reside at the center of all galaxies.When gas and stars fall into the supermassive black hole at the center of a galaxy, energy is released and is radiated away. In these cases the galaxy is said to host an active nucleus, hence the term Active Galactic Nuclei (AGN) for such galaxies. Large amounts of dust can absorb the emitted energy, and then re-radiate it in infrared wavelenths. Supermassive black holes can also launch relativistic jets, which are highly collimated outflows that and can extend up to Mpc distances into the intergalactic medium. In these jets, particles are accelerated to speeds very close to that of light, and emit across the electromagnetic spectrum, from radio to gamma rays. When the jet forms a small angle with the line of sight, relativistic effects boost the radiation from the jet to higher brightnesses and energies, and the jet is seen from the Earth as a blazar. Star formation is the second way that energy can be produced in the most luminous galaxies, and it is one of the most active research areas of both theoretical astrophysics and observational astronomy. The formulation of a theory of star formation is essential not only for understanding the origin of our own solar system and, ultimately, of life itself, but also for the development of a theory of galaxy formation and evolution. In galactic disks, stars are observed to form inside dense interstellar gas clouds consisting primarily of molecular hydrogen. Massive stars radiate primarily in ultraviolet and optical wavelengths. Star-forming regions are frequently enshrouded in dust, and a large fraction of the radiation from young massive stars is in this case absorbed by dust and re-emitted at IR wavelengths.In certain galaxies the rate of star formation is exceptionally high, and the radiative output from young stars can be comparable to that of an active nucleus. The study of such starburst galaxies is complicated by the frequent co-existence of black-hole related activity in the galaxy nucleus. The modeling of star forming regions and interpretation of observations in individual galaxies with high star-formation rates requires the use many different observations revealing the conditions in the interstellar medium, such as temperatures, densities, chemical composition, turbulent energy, and magnetic fields.The EuroCal project aims to bring together scientists from the University of Crete in Greece, the Max-Planck Institute for Radio Astronomy in Bonn, Germany, and Caltech in the US, working on both aspects of the physics of the most luminous galaxies, both from the theoretical and the observational angle. Our hope is to forge strong collaborations and to exchange data and expertise, so that we can start resolving the mysteries that enshroud the brightest galaxies in the Universe. Project EUROCAL is supported by the European Union’s Seventh Framework Programme, through an International Research Staff Exchange Scheme (IRSES) Marie Curie Action, under grant agreemen PIRSES-GA-2012-316788.