One of the important goals promising a major impact on the field of condensed matter and far beyond, is being able to describe properties of correlated fermionic systems quantitatively accurately without uncontrolled approximations. In this talk, I will focus on the family of diagrammatic Monte Carlo (DiagMC) methods introduced recently to meet this challenge. The Determinant DiagMC technique allowed to obtain the most accurate so far prediction of the critical temperature curve across the crossover from the Bardeen-Cooper-Schrieffer pairing to the Bose-Einstein condensate of molecules (the BCS-BEC crossover) in a two-component Fermi gas. A new generation of DiagMC methods based on sampling irreducible Feynman diagrams directly in the thermodynamic limit features an unprecedented tolerance to the notorious fermionic sign problem, which makes it a promising technique for unbiased solution of generic many-body fermionic systems. I will substantiate this promise with accurate results for the repulsive Hubbard model in the correlated Fermi liquid regime and a very recent calculation of the equation of state of the unitary Fermi gas.