This theory was originally developed by Lynn Margulis and there have been various discoveries that have supported it. One of the organelles thought to have been incorporated in this fashion is the mitochondria. Aspects of mitochondria that support this theory in that they have their own circular DNA, like prokaryotes, and their own ribosomes. When additional
mitochondria are needed for new daughter cells they are not constructed, but are duplicated “by a process that resembles binary fission in prokaryotes” (OpenStax College, 2013). These aspects seem to indicate that at one time mitochondria may have been independent prokaryotes that were incorporated into the communal ancestors of eukaryotes via endosymbiosis.
Another organelle, plastids, support the theory and are seen in eukaryotes that perform photosynthesis. Plastids are also not constructed when needed for new cells but divide in a fashion similar to mitochondria. Additionally, most eukaryotes plastids also contain a circular DNA chromosome and again, like we see in mitochondria, have their own ribosomes. The theory is that these plastids, seen to have initially evolved in cyanobacteria, were also introduced into eukaryotes through endosymbiosis.
One other example that shows this may have occurred in the past is that it has been seen that some algae become photosynthetic by taking in red or blue-green algae (OpenStax College, 2013). Seeing this occur would seem to support the theory that something similar may have occurred in the past and we are still seeing the development of the process in eukaryotes now.
The theory seems like a good one as in nature we regularly see symbiotic relationships with more complex organisms in nature, like bacteria in the gut necessary for digestion. With knowledge about microbial mats where prokaryotes exist in a sort of communal symbiosis, supporting one another by each performing their own functions, and the given density of organisms and the possibility of producing more productive relationships it would seem likely that this could occur. This, along with the knowledge that prokaryotes can share DNA through transformation or conjunction to potentially improve their function, would appear to support the idea that two individual prokaryotes could share DNA and functions together within a single cellular structure.
As with many things in the sciences it is hard to definitively state that this is what occurred. However, the positive evidence that supports endosymbiosis gives good grounds for the belief that this may have been a significant step in the evolution of eukaryotes.