There is a growing global need to shift from animal- towards plant-based diets. The main motivations are environmental/sustainability-, human health- and animal welfare concerns. The aim is to replace traditional animal-based food with various alternatives, predominantly plant-based analogs. The elevated consumption of fish and seafood, leads to negative impacts on the ecosystem, due to dwindling biodiversity, environmental damage and fish diseases related to large-scale marine farming, and increased intake of toxic substances, particularly heavy metals, which accumulate in fish due to water pollution. While these facts lead to increased awareness and rising dietary shifts towards vegetarian and vegan lifestyles, still the majority of seafood consumers seek traditional products. This encourages the development of plant-based analogs for fish and seafood, mimicking the texture and sensorial properties of fish-meat, seafood, or processed fish products. Mimicking the internal structure and texture of fish or seafood requires simulating their nanometric fibrous-gel structure. Common techniques of structuring plant-based proteins into such textures include hydrospinning, electrospinning, extrusion, and 3D printing. The conditions required in each technique, the physicochemical and functional properties of the proteins, along with the use of other non-protein functional ingredients are reviewed. Trends and possible future developments are discussed.