Link homology: from matrix factorizations to foam evaluation

So-called $\mathrm{sl}(n)$ link homology is a family of bigraded homology theories, one for each $n$, that have $\mathrm{sl}(n)$ quantum link invariants as the Euler characteristics. We'll review two constructions of these link homology theories. The original one uses matrix factorizations with potentials that are sums of powers of boundary variables, and the recent, due to Robert and Wagner, is based on a remarkable evaluation formula for closed foams.