The filoviruses, Marburg and Ebola, cause lethal hemorrhagic fever and are highest-priority bioterrorism agents. Filovirus particles contain a rod-like nucleocapsid and are normally filamentous, though other shapes are seen. It is poorly understood how such large filamentous particles are assembled and released from infected cells. Here we have studied Marburg virus production in infected cells using electron tomography. This technique allows virus particles to be visualized in three dimensions at different stages during assembly. We find that in early stages of virus production, highly infectious filamentous viruses are produced, whereas after prolonged infection poorly infectious spherical viruses are released. We also define the sequence of steps in filamentous virus release. The intracellular nucleocapsid first travels to the plasma membrane of the cell, where it binds laterally along its whole length. One end is then wrapped by the plasma membrane and wrapping proceeds rapidly until the virus protrudes vertically from the cell surface. The rear end of the virus particle then pinches off from the cell. We propose that other important filamentous and rod-shaped viruses also follow this series of steps of assembly and budding.