  The study of QFTs at finite density is hindered by the presence of the
so-called sign problem. The action definition of such systems is, in fact,
complex-valued making standard importance sampling Monte Carlo methods
ineffective. In this work, we shall review the generalized density of states
method for complex action systems and the Linear Logarithmic Relaxation
algorithm (LLR). We will focus on the recent developments regarding the bias
control of the LLR method and the evaluation of general observables in the
DoS+LLR framework. Recent results on the well-known relativistic Bose gas will
be presented, proving that in our approach the phase factor can be consistently
evaluated over hundreds of orders of magnitude. A first exploratory study on
the Thirring model in the DoS formalism will be presented as well.
