Quantum Chromodynamics (QCD) undergoes a crossover from the hadronic phase at low temperatures T to a quark-gluon plasma (QGP) phase at high T. This crossover and properties of the QGP phase are important for understanding the evolution of the early universe and are being studied by major Heavy Ion Collision (HIC) experiments at RHIC and LHC. The transition temperature and many QGP properties have been determined by Lattice QCD simulations. However, connecting these to experimental remnants of QGP fireballs produced at HICs is not straightforward. Thermal effects will modify the properties of the excitations (mesons and baryons) within the medium. We propose to investigate these in-medium changes using lattice QCD methods, shedding light onto the dynamics of HIC fireballs. Low temperature, high chemical potential phases are another region of the QCD phase diagram, interesting, e.g., for the physics of neutron stars. While this region is not accessible to numerical methods at present, we address the situation of an isospin chemical potential mu_I on the lattice, which also describes important aspects of neutron star cores. We propose to determine baryonic excitations for non-zero mu_I, which can provide a deeper understanding of possible quark matter cores in neutron stars.