The linker histone H1 and the histone variant H2A.Z are found throughout the eukaryotic kingdom. As ubiquitous components of chromatin, H1 and H2A.Z have been shown by in vitro and in vivo experiments to influence gene transcription and chromosome transmission in various organisms. The general and specific mechanisms for how H1 and H2A.Z exert their influence are incompletely described. Many of the fundamental roles of nucleosome and chromatin have been initially discovered using budding yeast. In this thesis I present experiments describing novel roles for histone H1 and H2A.Z in chromosome condensation and the control of transcription in yeast cells. To gain a sensitive and comprehensive view of H1’s influence on transcription in vegetatively growing yeast cells we used RNA-seq to compare mRNA levels in wild type cells to cells missing the HHO1 gene. In agreement with prior microarray studies, we find that mRNA levels of few genes are affected by two-fold or more due to loss of H1. However, we find that histone H1 modestly but significantly affects the transcription of approximately 15% of the genes in yeast. Notably, 90% of the genes whose transcription is significantly altered due to H1 loss exhibit increases in mRNA levels, indicating that H1 is a global repressor of transcription. Highly transcribed genes are more likely to be influenced by histone H1; we also observe a position effect, in which genes near telomeres are relatively unaffected by H1 presence. Histone H1 preferentially affects the transcription of stress-induced genes, and we find that strains lacking H1 are more sensitive to agents that elicit oxidative stress. Overall these results indicate that linker histone H1 cooperates with additional chromatin factors to broadly dampen gene expression. Chromosome condensation is essential for the fidelity of chromosome segregation during mitosis and meiosis. Condensation is associated with local changes in nucleosome structure, and larger scale alterations in chromosome topology mediated by the condensin complex. We examined the influence of linker histone H1 and variant histone H2A.Z on chromosome condensation in budding yeast cells. Linker histone H1 has been implicated in local and global compaction of chromatin in multiple eukaryotes, but we observe normal condensation of the rDNA locus in yeast strains lacking H1. However, deletion of the yeast HTZ1 gene, coding for variant histone H2A.Z, causes a significant defect in rDNA condensation. Loss of H2A.Z does not change condensin association with the rDNA locus, or significantly affect condensin mRNA levels. Prior studies reported that several phenotypes caused by loss of H2A.Z are suppressed by eliminating Swr1, a key component of the SWR complex that deposits H2A.Z in chromatin. We observe that a htz1∆ swr1∆ strain has near normal rDNA condensation. Unexpectedly, we find that elimination of the linker histone H1 can also suppress the rDNA condensation defect of htz1∆ strains. Loss of H1 also causes an allele-specific suppression of the growth defects seen in temperature sensitive alleles of the BRN1 condensin gene. Our experiments demonstrate that H2A.Z promotes chromosome condensation, in part by counteracting activities of histone H1 and the SWR complex. Overall this work has defined new functions for the H1 and H2A.Z, and the systems we have developed provide valuable launching pads for further examination of their specific influences on transcription and chromosome transmission.