this panoramic overview a more detailed (but certainly not complete) account of two problems: intrinsic ergodicity and density of ergodic measures for systems with specification-like properties. Both are related to the structure of the simplex of invariant measures of the dynamical system. The first problem is, broadly speaking, a question about the relation between specification-like properties and entropy, both topological and measure-theoretic. One of the first results obtained using specification was that this property together with expansiveness implies the uniqueness of a measure of maximal entropy. Recall that the Variational Principle states that the *topological entropy* ${h_\textrm{top}}(T)$ of a compact dynamical system $(X,T)$ equals the supremum over the set of all measure-theoretic entropies $h_\mu(T)$ where $\mu$ runs through all $T$-invariant Borel probability measures on $X$. An invariant measure which achieves this supremum is called the *measure of maximal entropy* for $(X,T)$. A dynamical system $(X,T)$ is *intrinsically ergodic* if it has a unique measure of maximal entropy. We discuss related results in connection with other specification-like properties.

The second problem is an instance of one of the most basic questions in the theory of dynamical systems: *Given a dynamical system, classify and study the properties of invariant measures.* In case 