Final answer:
Eukaryotes evolved around 2 billion years ago during the Proterozoic Eon, and this development is supported by the endosymbiotic theory. Fossil records and genetic evidence suggest a close relationship between early eukaryotes and the domain Archaea.
Step-by-step explanation:
Eukaryotes, the complex cells with a nucleus and internal membrane-bound organelles, evolved approximately 2 billion years ago during the Proterozoic Eon. This significant evolutionary step is explained by the endosymbiotic theory, which proposes that eukaryotic organelles such as mitochondria and chloroplasts originated from free-living prokaryotic organisms. While the oldest fossil evidence related to modern eukaryotes is a red alga dating back 1.2 billion years, most scientific evidence supports the idea that eukaryotic cells emerged about 2 billion years ago. These early eukaryotes likely descended from an ancestor with archaean biochemistry and membrane structure, which suggests a close relationship between Archaea and Eukarya domains.
As for multicellularity, it is believed to have evolved among eukaryotes approximately 1.5 billion years ago, leading to the vast diversity we observe today. The early biochemical pathways related to photosynthesis in prokaryotic cells laid the foundation for this process in eukaryotic cells, highlighting the interconnected evolution of life on Earth.