Bacterial genomes commonly contain 'addiction' gene complexes that code for both a toxin and a corresponding antitoxin. As long as both genes are expressed, cells carrying the complex can remain healthy. However, loss of the complex (including segregational loss in daughter cells) can entail death of the cell. We develop a theoretical model to explore a number of evolutionary puzzles posed by toxin-antitoxin (TA) population biology. We first extend earlier results demonstrating that TA complexes can spread on plasmids, as an adaptation to plasmid competition in spatially structured environments, and highlight the role of kin selection. We then considered the emergence of TA complexes on plasmids from previously unlinked toxin and antitoxin genes. We find that one of these traits must offer at least initially a direct advantage in some but not all environments encountered by the evolving plasmid population. Finally, our study predicts non-transitive 'rock-paper-scissors' dynamics to be a feature of intragenomic conflict mediated by TA complexes. Intragenomic conflict could be sufficient to select deleterious genes on chromosomes and helps to explain the previously perplexing observation that many TA genes are found on bacterial chromosomes.