The Thurston norm is a measure of the combinatorial complexity of embedded surfaces representing second homology classes in a link complement. We will present results based on Heegaard Floer theory which determine the Thurston norms of members of a four-parameter family of pretzel links. We will also discuss two theorems descrbing how local changes in a link affect its Thurston norm and use these to extend the pretzel results to a broader class of links.