Some of the most important outstanding problems in fundamental physics involve the calculation of transport properties of strongly correlated Fermions at finite temperature, encountered for example in nuclear matter at non-zero baryon density and high-Tc superconductivity in the cuprates. These problems have remained theoretically unsolved despite decades of concerted efforts. Quantum simulation offers the hope to solving strongly-correlated quantum problems, but so far the degree of programmability of experiments has not been sufficient to tackle these specific problems. In this talk, I will discuss three advances towards the simulation of transport properties of Fermions at finite temperature. In the first part, I will show the largest digital simulation of a fermionic model to date [1], implementing a building block for finite-temperature simulations based on quantum-computer assisted Monte Carlo [2,3]. In the second part, I will discuss the first observation of a finite temperature phase transition in one spatial dimension [4] fifty years after its prediction [5]. Finally, I will discuss the extraction of transport coefficients in a long-range interacting spin model using a trapped-ion quantum simulator [6]. [1] Hemery et al., arXiv: 2309.10552 (2023) [2] Lu, Banuls, Cirac, PRX Quantum (2021) [3] Schuckert et al., PRB L (2023) [4] Schuckert, Katz, et al., arXiv:2310.19869 (2023) [5] Dyson, Commun.Math. Phys. (1971), Thouless, Phys. Rev. (1969) [6] Joshi et al, Science (2022)