Exceptions to paradigms are important in at least two ways, including highlighting limits of existing paradigms and in providing novel opportunities to test general hypotheses. In the context of genetic processes and systems, non-paradigmatic processes such as complex patterns of inheritance can reveal what may be overlooked in conventional systems and even inform us about established general ideas in evolutionary and population genetics. This thesis explores the potential of non-paradigmatic genetic systems as valuable tools for understanding evolutionary processes. In Chapters 1 and 2, I focus on an atypical genetic system in arthropods with genetic peculiarities that allow for less biased natural experiments for testing hypotheses regarding several fundamental questions regarding selection, mutation, and drift, and about sex determination system turnover. To highlight this system’s use for several fundamental evolutionary questions, chapter 1 presents the power of X chromosomes for evolutionary analysis, the limitations of this approach, and how the atypical system resolves these limitations. I first present both the value in comparing sex chromosomes to autosomes, and the challenges in interpreting data from these studies due to the co-occurrence of confounding differences between X chromosomes and autosomes— primarily the hemizygosity of the X chromosome in XY males, and the unequal transmission of X chromosomes through the sexes. I describe ways in which this confounded problem has been previously addressed, then introduce an atypical arthropod genetic system and explain how the system allows for the isolation of hemizygosity as a driver of X chromosome and autosomal difference. Finally, I discuss the implications of potential findings in evolutionary rate, sequence diversity, and codon bias. In Chapter 2, I employ the same exceptional genetic system in arthropods in comparison to relatives with typical genetic systems to test a very different question, namely the origins of haplodiploidy. In this chapter, I specifically investigate the origins of male-haploid systems and the relationship of gene-rich X chromosomes with sex-determination system turnover and find evidence to support intragenomic conflict as a driver of turnover. Intragenomic conflict is generally understudied and its effects on evolutionary processes, potentially substantial, remain largely untested. Thus, I offer some of the first empirical testing of its contribution to major genetic and evolutionary shifts. In Chapter 3, I study the history of a gene fusion of two enzymes involved in subsequent steps of fungal leucine biosynthesis, an essential metabolic process in fungi, through phylogenetic reconstruction on the fusion domains. I find a very complex history, featuring ancestral fusion, multiple instances of gene fission and loss, and abundant gain of the fused construct through horizontal gene transfer. This result is somewhat surprising given the core nature of these enzymes and longstanding paradigms of eukaryotic metabolic and genic evolution. Altogether, this doctoral body of work aims to demonstrate the value in studying exceptional genetic systems and evolutionary processes and how they are revealing for a broad set of important ideas in molecular evolution and genetics.