The spread of viral pathogens both between and within hosts is inherently a spatial process. While the spatial aspects of viral spread at the epidemiological level have been increasingly well characterized, the spatial aspects of viral spread within infected hosts are still understudied. Recent experimental studies, however, have started to shed more light on the mechanisms and spatial dynamics of viral spread within hosts. Here, we review these experimental studies as well as the limited number of computational modeling efforts that have begun to integrate spatial considerations for understanding within-host viral spread. We limit our review to influenza virus to highlight key mechanisms affecting spatial aspects of viral spread for pathogens of the respiratory tract. There is considerable empirical evidence for highly spatial within-host spread of influenza virus, yet few computational modeling studies that shed light on possible factors that structure the dynamics of this spatial spread. In existing modeling studies, there is also a striking absence of theoretical expectations of how spatial dynamics may impact the dynamics of viral populations. To mitigate this, we turn to the extensive ecological and evolutionary literature to provide informed theoretical expectations for what viral and host factors may impact the spatial patterns of within-host viral dynamics and for how spatial spread will affect the genetic composition of within-host viral populations. We end by discussing current knowledge gaps related to the spatial component of within-host influenza virus spread and the potential for within-host spatial considerations to inform the development of disease control strategies.