The author characterizes Heyting algebras with a modular congruence lattice. His investigations are carried out within the Priestley space \(X\) of such algebras. The author also looks at Heyting algebras with complemented congruence or subalgebra lattices. For example, for finite Heyting spaces \(X\), \(\text{Con} (X)\) is complemented if and only if \(X\) is a tree and for a Heyting algebra \(H\), \(\text{Sub} (H)\) is complemented in case that \(H\) is retractive, i.e., for each epimorphism \(H\to H'\), there is an embedding \(H'\to H\) such that \(H'\to H\to H'\) is the identity map.