Protein arginine methylation is an abundant post-translational modification catalyzed by protein arginine methyltransferases (PRMTs). Arginine methylation plays important roles in a variety of cellular pathways and human diseases. PRMT1, the predominant PRMT, catalyzes approximately 85% of all protein arginine methylation in vivo. While many details of how PRMT1 functions have been uncovered through the past two decades, there are many details which remain unclear, including how arginine methylation is regulated, how PRMT1 binds substrates, and what role PRMTs play in RNA surveillance. Our recent data presented in this thesis showed that reduction of the PRMT1 enzyme, following recombinant expression and purification, changes both enzymatic activity and oligomeric state. A cysteine residue(s) was found to be responsible for the observed redox chemistry in PRMT1 and at least one parameter in the kinetic mechanism, S-adenosylmethionine (AdoMet) binding, was faster with a reduced enzyme. This work suggests exciting potential for the regulation of PRMTs in vivo by oxidative stress. In addition to studying the effects of reduction/oxidation on PRMT1, a foundation for future experiments was laid. These experiments investigate substrate recognition by PRMTs and what the role arginine methylation may play in RNA processing and surveillance. To better understand how PRMTs selectively bind a wide variety of substrates, I have designed and preliminarily characterized several Hmt1 (the S. cerevisiae homologue of PRMT1) variants. These variants will be used for crystallization trials of a homogeneous complex, containing Hmt1, AdoMet, and a peptide substrate, capable of revealing specific chemical interactions between Hmt1 and the peptide substrate. To further our understanding of Hmt1's role in RNA processing and surveillance, particularly in RNA degradation pathways, I extracted yeast RNA from both wild type and Hmt1-null cells. The RNA was probed using a S. cerevisiae whole-genome microarray. This analysis revealed that Hmt1 exhibits statistically significant effects in several broad areas including molecular function, biological processes, cellular components, and some KEGG pathways. The presented studies have revealed the exciting potential for an in vivo regulatory mechanism of PRMT1 and each study is primed for further investigation both in vivo and in vitro.