The recent discovery in 2012 at the LHC of a particle with a mass of about 125 GeV and properties that are compatible with a Standard Model-like Higgs boson has started a new era of particle physics. An e+e- Linear Collider (LC) with a centre-of-mass energy that can be raised to at least up to 500 GeV is ideally suited for studying the properties of this new particle with high precision and posses also a rich physics programme of top and electroweak precision physics . Currently the most mature design for such a high-energy precision machine is the International Linear Collider (ILC). Still no explicit signs for physics beyond the Standard Model have been found neither at the LHC nor at the low-energy experiments. Nevertheless, the Standard Model leaves many questions open and both high precision calculations as well as precision measurements may trace the path to the true underlying physics model. One excellent candidate for explaining most of the open questions is Supersymmetry (SUSY) that establishes a new symmetry between fermions and bosons. Such an excting new physics model is still a hot candidate in numerous ongoing experimental analyses world-wide, in particular at the LHC. However its discovery may be very challenging. The high-luminosity LC, however, offers also a unique potential for discoveries of physics beyond the Standard Model. With its specific design features as beam polarization, tunable energy, etc., the ILC may be the crucial partner of the LHC for hunting SUSY.