Riesz homomorphisms represent a pivotal class of homomorphisms within vector lattices. This talk explores their extensions and various generalizations on more complex structures such as order unit spaces, which are pre-Riesz spaces capable of being densely embedded in Riesz spaces of continuous functions. Our discussion will delve into the extensions of these homomorphisms to larger vector lattices, examining their interplay with extreme rays of dual cones, point evaluations, and positive disjointness preserving operators.