This thesis focusses on two classes of systems that exhibit non-Fermi liquid behaviour in experiments: we investigated aspects of chiral ferromagnets and of antiferromagnetic metals close to a quantum critical point. In chiral ferromagnets, the absence of inversion symmetry makes spin-orbit coupling possible, which leads to a helical modulation of the ferromagnetically ordered state. We studied the motion of electrons in the magnetically ordered state of a metal without inversion symmetry by calculating their generic band-structure. We found that spin-orbit coupling, although weak, has a profound effect on the shape of the Fermi surface: On a large portion of the Fermi surface the electron motion parallel to the helix practically stops. Signatures of this effect can be expected to show up in measurements of the anomalous Hall effect. Recent neutron scattering experiments uncovered the existence of a peculiar kind of partial order in a region of the phase diagram adjacent to the ordered state of the chiral ferromagnet MnSi. Starting from the premise that this partially ordered state is a thermodynamically distinct phase, we investigated an extended Ginzburg-Landau theory for chiral ferromagnets. In a certain parameter regime of the Ginzburg-Landau theory we identified crystalline phases that are reminiscent of the so-called blue phases in liquid crystals. Many antiferromagnetic heavy-fermion systems can be tuned into a regime where they exhibit non-Fermi liquid exponents in the temperature dependence of thermodynamic quantities such as the specific heat capacity; this behaviour could be due to a quantum critical point. If the quantum critical behaviour is field-induced, the external field does not only suppress antiferromagnetism but also induces spin precession and thereby influences the dynamics of the order parameter. We investigated the quantum critical behavior of clean antiferromagnetic metals subject to a static, spatially uniform external magnetic field. We studied how the interplay of precession and damping affects various thermodynamic and transport quantities. We found that the susceptibility d M/d B is the thermodynamic quantity which shows the most significant change upon approaching the quantum critical point and which gives experimental access to the (dangerously irrelevant) spin-spin interactions. Finally, we studied the quantum critical behaviour of two-dimensional antiferromagnetic metals. Going beyond an order parameter theory, we included the electronic quasiparticles as well as the fluctuating magnetization in a functional Renormalization Group calculation. Preliminary results indicate a divergence in the fRG-equations already at a finite distance from the quantum critical point - this is incompatible with the Hertz-Millis picture
