  Recent results on the Racah algebra $\mathcal{R}_n$ of rank $n - 2$ are
reviewed. $\mathcal{R}_n$ is defined in terms of generators and relations and
sits in the centralizer of the diagonal action of $\mathfrak{su}(1,1)$ in
$\mathcal{U}(\mathfrak{su}(1,1))^{\otimes n}$. Its connections with
multivariate Racah polynomials are discussed. It is shown to be the symmetry
algebra of the generic superintegrable model on the $ (n-1)$ - sphere and a
number of interesting realizations are provided.
