Marine biopolymers, abundantly present in seaweeds and marine animals, feature diverse structures and functionalities, and possess a wide range of beneficial biological activities. Characterized by high biocompatibility and biodegradability, as well as unique physicochemical properties, marine biopolymers are attracting a constantly increasing interest for the development of advanced systems for applications in the biomedical field. The development of electrospinning offers an innovative technological platform for the production of nonwoven nanofibrous scaffolds with increased surface area, high encapsulation efficacy, intrinsic interconnectivity, and structural analogy to the natural extracellular matrix. Marine biopolymer-based electrospun nanofibrous scaffolds with multifunctional characteristics and tunable mechanical properties now attract significant attention for biomedical applications, such as tissue engineering, drug delivery, and wound healing. The present review, covering the literature up to the end of 2021, highlights the advancements in the development of marine biopolymer-based electrospun nanofibers for their utilization as cell proliferation scaffolds, bioadhesives, release modifiers, and wound dressings.