does eukaryotes have specialized structures or internal compartments
Yes, they have long slender motile cytoplasmic projections, called flagella, or similar structures called cilia.
Eukaryote
Many eukaryotes have long slender motile cytoplasmic projections, called flagella, or similar structures called cilia.
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Eukaryote [SEP] Cytoskeletal structures
Many eukaryotes have long slender motile cytoplasmic projections, called flagella, or similar structures called cilia. Flagella and cilia are sometimes referred to as undulipodia, and are variously involved in movement, feeding, and sensation. They are composed mainly of tubulin. These are entirely distinct from prokaryotic flagellae. They are supported by a bundle of microtubules arising from a centriole, characteristically arranged as nine doublets surrounding two singlets. Flagella also may have hairs, or mastigonemes, and scales connecting membranes and internal rods. Their interior is continuous with the cell's cytoplasm. Microfilamental structures composed of actin and actin binding proteins, e.g., α-actinin, fimbrin, filamin are present in submembranous cortical layers and bundles, as well.