Although Importance Sampling techniques for lattice QCD have matured over the last thirty years, quantum field theories with an overlap or a sign problem are beyond the grasp of Markov Chain Monte Carlo simulations. Non-Markovian Random Walks might bridge this gap. Among those is the density-of-states approach. In my talk, I will introduce its LLR version. I will illustrate, using the q=20 state Potts model, to what extent overlap problems are solved. For finite density QFTs, the partition function appears as a Fourier transform of the density-of-states. Using the Z3 theory at finite densities and heavy-dense QCD, I will show that the LLR formulation provides enough precision to solve the strong sign problem without reformulation or complexification.