A considerable part of the diversity of eukaryotic phototrophs consists of algae with plastids that evolved from endosymbioses between two eukaryotes. These complex plastids are characterized by a high number of envelope membranes (more than two) and some of them contain a residual nucleus of the endosymbiotic alga called a nucleomorph. Complex plastid-bearing algae are thus chimeric cell assemblies, eukaryotic symbionts living in a eukaryotic host. In contrast, the primary plastids of the Archaeplastida (plants, green algae, red algae, and glaucophytes) possibly evolved from a single endosymbiosis with a cyanobacterium and are surrounded by two membranes. Complex plastids have been acquired several times by unrelated groups of eukaryotic heterotrophic hosts, suggesting that complex plastids are somewhat easier to obtain than primary plastids. Evidence suggests that complex plastids arose twice independently in the green lineage (euglenophytes and chlorarachniophytes) through secondary endosymbiosis, and four times in the red lineage, first through secondary endosymbiosis in cryptophytes, then by higher-order events in stramenopiles, alveolates, and haptophytes. Engulfment of primary and complex plastid-containing algae by eukaryotic hosts (secondary, tertiary, and higher-order endosymbioses) is also responsible for numerous plastid replacements in dinoflagellates. Plastid endosymbiosis is accompanied by massive gene transfer from the endosymbiont to the host nucleus and cell adaptation of both endosymbiotic partners, which is related to the trophic switch to phototrophy and loss of autonomy of the endosymbiont. Such a process is essential for the metabolic integration and division control of the endosymbiont in the host. Although photosynthesis is the main advantage of acquiring plastids, loss of photosynthesis often occurs in algae with complex plastids. This chapter summarizes the essential knowledge of the acquisition, evolution, and function of complex plastids.