Chloroplasts originated just once, from cyanobacteria enslaved by a biciliate protozoan to form the plant kingdom (green plants, red and glaucophyte algae), but subsequently, were laterally transferred to other lineages to form eukaryote–eukaryote chimaeras or meta–algae. This process of secondary symbiogenesis (permanent merger of two phylogenetically distinct eukaryote cells) has left remarkable traces of its evolutionary role in the more complex topology of the membranes surrounding all non–plant (meta–algal) chloroplasts. It took place twice, soon after green and red algae diverged over 550 Myr ago to form two independent major branches of the eukaryotic tree (chromalveolates and cabozoa), comprising both meta–algae and numerous secondarily non–photosynthetic lineages. In both cases, enslavement probably began by evolving a novel targeting of endomembrane vesicles to the perialgal vacuole to implant host porter proteins for extracting photosynthate. Chromalveolates arose by such enslavement of a unicellular red alga and evolution of chlorophyll c to form the kingdom Chromista and protozoan infrakingdom Alveolata, which diverged from the ancestral chromalveolate chimaera. Cabozoa arose when the common ancestor of euglenoids and cercozoan chlorarachnean algae enslaved a tetraphyte green alga with chlorophyll a and b. I suggest that in cabozoa the endomembrane vesicles originally budded from the Golgi, whereas in chromalveolates they budded from the endoplasmic reticulum (ER) independently of Golgi–targeted vesicles, presenting a potentially novel target for drugs against alveolate Sporozoa such as malaria parasites and Toxoplasma. These hypothetical ER–derived vesicles mediated fusion of the perialgal vacuole and rough ER (RER) in the ancestral chromist, placing the former red alga within the RER lumen. Subsequently, this chimaera diverged to form cryptomonads, which retained the red algal nucleus as a nucleomorph (NM) with approximately 464 protein–coding genes (30 encoding plastid proteins) and a red or blue phycobiliprotein antenna pigment, and the chromobiotes (heterokonts and haptophytes), which lost phycobilins and evolved the brown carotenoid fucoxanthin that colours brown seaweeds, diatoms and haptophytes. Chromobiotes transferred the 30 genes to the nucleus and lost the NM genome and nuclear–pore complexes, but retained its membrane as the periplastid reticulum (PPR), putatively the phospholipid factory of the periplastid space (former algal cytoplasm), as did the ancestral alveolate independently. The chlorarachnean NM has three minute chromosomes bearing approximately 300 genes riddled with pygmy introns. I propose that the periplastid membrane (PPM, the former algal plasma membrane) of chromalveolates, and possibly chlorarachneans, grows by fusion of vesicles emanating from the NM envelope or PPR. Dinoflagellates and euglenoids independently lost the PPM and PPR (after diverging from Sporozoa and chlorarachneans, respectively) and evolved triple chloroplast envelopes comprising the original plant double envelope and an extra outermost membrane, the EM, derived from the perialgal vacuole. In all metaalgae most chloroplast proteins are coded by nuclear genes and enter the chloroplast by using bipartite targeting sequences – an upstream signal sequence for entering the ER and a downstream chloroplast transit sequence. I present a new theory for the four–fold diversification of the chloroplast OM protein translocon following its insertion into the PPM to facilitate protein translocation across it (of both periplastid and plastid proteins). I discuss evidence from genome sequencing and other sources on the contrasting modes of protein targeting, cellular integration, and evolution of these two major lineages of eukaryote ‘cells within cells’. They also provide powerful evidence for natural selection's effectiveness in eliminating most functionless DNA and therefore of a universally useful non–genic function for nuclear non–coding DNA, i.e. most DNA in the biosphere, and dramatic examples of genomic reduction. I briefly argue that chloroplast replacement in dinoflagellates, which happened at least twice, may have been evolutionarily easier than secondary symbiogenesis because parts of the chromalveolate protein–targeting machinery could have helped enslave the foreign plastids.