Lattice QCD is the most suitable tool to make quantitative predictions about non-perturbative phenomena of Quantum Chromodynamics (QCD). Unfortunately, due to the sign problem, QCD at finite density is not yet accessible to Monte Carlo simulations on the lattice. However, in simpler systems one can use a dual representation to avoid the sign problem and make Monte Carlo techniques applicable. In the first part of this work we investigate two effective theories of QCD. The first model, the "SU(3) spin model'', is obtained from the strong coupling approximation of the gauge action and the hopping expansion of the fermion determinant. It has Polyakov loops as degrees of freedom and inherits the main properties of QCD related to center symmetry and the sign problem.?The second model, the "Z(3) spin model'', uses the Svetitsky-Yaffe conjecture and reduces the previous model to a 3-state Potts model with magnetic field and chemical potential. We developed new Monte Carlo algorithms for the dual representation and explore the phase diagrams in the temperature-density plane. In particular we discuss two different generalizations of the Prokof'ev-Svistunov algorithm.In the second part of this work we present the surface worm algorithm (SWA) and assess its performance in comparison to local dual updates. The SWA is an extension of the Prokof'ev-Svistunov algorithm to simulate systems with loops and surfaces and we use it for the dual representation of Abelian Gauge-Higgs models with chemical potential. The last part is an independent project done during the secondment in Wuppertal. It was motivated by the study of chiral symmetry restoration at finite temperature in the chiral limit. We use overlap fermions to have good chiral properties on the lattice. Before performing large scale simulations, one needs to optimize the algorithms. In this part we focused on the improvement of the Conjugate Gradient and the eigenvalue problem solver.