This paper is an interesting survey, concerning the representation of lattices as lattices of congruences and as lattices of equational theories. For an algebra \(A\), \(\text{Con}(A)\) is the lattice of congruence relations, \(\text{Eq}(A)\) the lattice of equivalence relations on \(A\). Every algebraic lattice \(L\) has a representation as a type 3 complete sublattice of some \(\text{Eq}(A)\). If \(L\) is in addition modular, then \(L\) has a representation as a type 2 complete sublattice of some \(\text{Eq}(A)\). \(L\) is an algebraic lattice iff there exists an algebra \(A\) having type 3 congruence joins such that \(\text{Con}(A)\) is isomorphic to \(L\). Also, \(A\) can be chosen such that \(\Aut(A)\) is isomorphic to any given group. If \(D\) is a finite distributive lattice, then there is a finite groupoid \(A\) with \(\text{Con}(A)\) isomorphic to \(D\). If \(D\) is an algebraic distributive lattice then there is a semigroup \(A\) with \(\text{Con}(A)\) isomorphic to \(D\). Further definitions are needed, concerning results on similarity type, compact 1, lattices of equational theories. Some problems and conjectures are stated.