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In this note we overview recent convergence results for correlations in thecritical planar nearest-neighbor Ising model. We start with a short discussionof the combinatorics of the model and a definition of fermionic and spinorobservables. After that, we illustrate our approach to spin correlations by aderivation of two classical explicit formulae in the infinite-volume limit.Then we describe the convergence results (as the mesh size tends to zero, inarbitrary planar domains) for fermionic correlators, energy-density and spinexpectations. Finally, we discuss scaling limits of mixed correlators involvingspins, disorders and fermions, and the classical fusion rules for them.

2D Ising model: correlation functions at criticality via Riemann-type boundary value problems