Convolvulaceae, the morning glories or bindweeds, is a large family containing species of economic value, including crops, traditional medicines, ornamentals, and vegetables. However, not only are the phylogenetic relationships within this group still debated at the intertribal and intergeneric levels, but also plastid genome (plastome) complexity within Convolvulaceae is not well surveyed. We gathered 78 plastomes representing 17 genera across nine of the 12 Convolvulaceae tribes. Our plastid phylogenomic trees confirm the monophyly of Convolvulaceae, place the genus Jacquemontia within the subfamily Dicranostyloideae, and suggest that the tribe Merremieae is paraphyletic. In contrast, positions of the two genera Cuscuta and Erycibe are uncertain as the bootstrap support of the branches leading to them is moderate to weak. We show that nucleotide substitution rates are extremely variable among Convolvulaceae taxa and likely responsible for the topological uncertainty. Numerous plastomic rearrangements are detected in Convolvulaceae, including inversions, duplications, contraction and expansion of inverted repeats (IRs), and losses of genes and introns. Moreover, integrated foreign DNA of mitochondrial origin was found in the Jacquemontia plastome, adding a rare example of gene transfer from mitochondria to plastids in angiosperms. In the IR of Dichondra, we discovered an extra copy of rpl16 containing a direct repeat of ca. 200 bp long. This repeat was experimentally demonstrated to trigger effective homologous recombination, resulting in the coexistence of intron-containing and -lacking rpl16 duplicates. Therefore, we propose a hypothetical model to interpret intron loss accompanied by invasion of direct repeats at appropriate positions. Our model complements the intron loss model driven by retroprocessing when genes have lost introns but contain abundant RNA editing sites adjacent to former splicing sites.