Chromatin and chromosomes of fungi are highly diverse and dynamic, even within species. Much of what we know about histone modification enzymes, RNA interference, DNA methylation, and cell cycle control was first addressed in Saccharomyces cerevisiae, Schizosaccharomyces pombe, Aspergillus nidulans and Neurospora crassa. Here, we examine the three landmark regions that are required for maintenance of stable chromosomes and their faithful inheritance, namely origins of DNA replication, telomeres and centromeres. We summarize the state of recent chromatin research that explains what is required for normal function of these specialized chromosomal regions in different fungi, with an emphasis on silencing mechanism associated with subtelomeric regions, initiated by sirtuin histone deacetylases and histone H3 lysine 27 (H3K27) methyltransferases. We explore mechanisms for the appearance of “accessory” or “conditionally dispensable” chromosomes, and contrast what has been learned from studies on genome-wide chromosome conformation capture in Saccharomyces cerevisiae, Schizosaccharomyces pombe, Neurospora crassa and Trichoderma reesei. While most of the current knowledge is based on work in a handful of genetically and biochemically tractable model organisms, we suggest where major knowledge gaps remain to be closed. Fungi will continue to serve as facile organisms to uncover the basic processes of life because they make excellent model organisms for genetics, biochemistry, cell biology and evolutionary biology.