Jordan homomorphisms between two associative algebras are linear maps which preserve squares. This dissertation studies Jordan homomorphisms between structural matrix algebras (SMAs), which are unital subalgebras of \(M_n\) (the algebra of all complex square matrices of order \(n\)) spanned by some set of matrix units. The first objective of the dissertation is to completely describe the form of all Jordan embeddings between two SMAs using concepts introduced by Coelho’s description of SMA automorphisms. Secondly, continuing the work of Molnar and Šemrl on rank-one preservers of the algebra of uppertriangular matrices \(\mathcal{T}_n\), it considers several natural linear preserver problems on SMAs and puts them into the broader context of Jordan embeddings on SMAs. The third part of the dissertation contains a full extension of the well-known nonlinear preserver results of Petek and Šemrl (on \(M_n\) and \( \mathcal{T}_n \)) in the context of SMAs. More precisely, a characterization of SMAs \(\mathcal{A} \subseteq M_n\) is obtained with the property that all injective continuous commutativity and spectrum preserving map \(\mathcal{A} \to M_n\) are necessarily Jordan embeddings.