Simulations with exact and chirally improved fermions

We review simulations of lattice of QCD with chiral invariant overlap fermions and chirally improved maximally twisted mass fermions. We discuss simulations with twisted mass fermions for Nf=2 flavours of mass degenerate quarks and for the situation of Nf=2+1+1 flavours, where the strange and the charm quarks are taken into account as active degrees of freedom. Results are presented for a number of physical quantities among which are the muon anomalous magnetic moment, pseudo scalar masses and decay constants, quark masses, the pion scattering length and the ρ-meson resonance. In addition, we discuss aspects of the simulations themselves and the non-perturbative renormalization that has been performed. Finally, first result are given for simulations directly at the physical value of the pion mass.