Leishmania are kinetoplastid pathogens that cause leishmaniasis, a debilitating and potentially life-threatening infection if untreated. Unusually, Leishmania regulate their gene expression largely post-transcriptionally due to the arrangement of their coding genes into polycistronic transcription units that may contain 100s of functionally unrelated genes. Yet, Leishmania are capable of rapid and responsive changes in gene expression to challenging environments, often instead correlating with dynamic changes in their genome composition, ranging from chromosome and gene copy number variations to the generation of extrachromosomal DNA and the accumulation of point mutations. Typically, such events indicate genome instability in other eukaryotes, coinciding with genetic abnormalities, but for Leishmania, exploiting these products of genome instability can provide selectable substrates to catalyse necessary gene expression changes by modifying gene copy number. Unorthodox DNA replication, DNA repair, replication stress factors and DNA repeats are recognised in Leishmania as contributors to this intrinsic instability, but how Leishmania regulate genome plasticity to enhance fitness whilst limiting toxic under- or over-expression of co-amplified and co-transcribed genes is unclear. Herein, we focus on fresh, and detailed insights that improve our understanding of genome plasticity in Leishmania. Furthermore, we discuss emerging models and factors that potentially circumvent regulatory issues arising from polycistronic transcription. Lastly, we highlight key gaps in our understanding of Leishmania genome plasticity and discuss future studies to define, in higher resolution, these complex regulatory interactions.