A free-living cyanobacterium (above) lies next to its brethren from a distant past, now a chloroplast coiled up and trapped (for good) within a eukaryotic cell (bottom). The chloroplast still has remnants of the cyanobacterial genome, with a greatly reduced gene set. Both bacterial inner and outer membranes have also been retained -- which is how both plastids and mitochondria usually have a double membrane. The most bacterial-like of the plastids belong to Glaucophytes, a small group of deep-branching algae. These plastids have retained the bacterial peptidoglycan (wall material) layer, between the two membranes. This, along with their vibrant blue-green colour, earns them a distinct name: cyanelles.
Pretty much every photosynthetic eukaryote you see shares one single common origin of plastid endosymbiosis, with the exception of a testate amoeba -- Paulinella chromatophora, which has one or two recently reduced cyanobacteria ('cyanelles', again) of a separate origin. There is a relatively large interest (reads: a couple labs) in Paulinella in hopes that studying it will reveal something about how plastid endosymbiosis works, as well as some insights to how the other (main) symbiosis event happened. Eukaryotes have thus domesticated cyanobacteria on at least two separate occasions, and seem to be doing fairly well with their stolen agriculture industry.