A hypha consists of one or more cells surrounded by a tubular cell wall. In most fungi, hyphae are divided into cells by internal cross-walls called septa (singular septum). Septa are usually perforated by pores large enough for ribosomes, mitochondria and sometimes nuclei to flow among cells. The structural polymer in fungal cell walls is typically chitin (in contrast plants have cellulosic cell walls, and animal cells lack walls). Some Fungi however, have non septate hypha, meaning their hypha are not separated by septa.

Hyphae grow at their tips. During tip growth, cell walls are extended by the external assembly and polymerization of cell wall components, and the internal production of new cell membrane. The spitzenkörper is an intracellular organelle associated with tip growth. It is composed of an aggregation of membrane-bound vesicles containing cell wall components. The spitzenkörper is part of the endomembrane system of fungi, holding and releasing vesicles it receives from the Golgi apparatus, which then travel to the cell membrane via the cytoskeleton, and dump their contents outside the cell by the process of exocytosis. Vesicle membranes contribute to growth of the cell membrane while their contents form new cell wall. The spitzenkörper moves along the apex of the hyphal strand and generates apical growth and branching; the apical growth rate of the hyphal strand parallels and is regulated by the movement of the spitzenkörper.

As a hypha extends, septa may be formed behind the growing tip to partition each hypha into individual cells. Hyphae can branch through bifurcation of a growing tip, or by the emergence of a new tip from an established hypha.

Hyphae may be modified in many different ways to serve specific functions. Some parasitic fungi form haustoria that function in absorption within the host cells. The arbuscules of mutualistic mycorrhizal fungi serve a similar function in nutrient exchange, so are important in assisting nutrient and water absorption by plants. Hyphae are found enveloping the gonidia in lichens, making up a large part of their structure. In nematode-trapping fungi, hyphae may be modified into trapping structures such as constricting rings and adhesive nets. Cords can be formed to transfer nutrients over larger distances.

Classification based on cell division

• Septate (with septa)
• Pseudohyphae are not true septate hyphae and are distinguished from "true hyphae" by their method of growth, relative frailty and lack of cytoplasmic connection between the cells. They are most often found in yeasts as the result of a sort of incomplete budding where the cells remain attached after division.
• Aseptate or coenocytic (without septa).