Estimation of viral parameters, such as the basic reproductive number (R0) and infected cell life span, is central to the quantitative study of the within–host dynamics of viral diseases such as human immunodeficiency virus, hepatitis B or hepatitis C. As these parameters can rarely be determined directly, they are usually estimated indirectly by fitting mathematical models to viral load data. This paper investigates how parameter estimates obtained by such procedures depend on the assumptions made concerning the viral life cycle. It finds that estimates of the basic reproductive number obtained using viral load data collected during the initial stages of infection can depend quite sensitively on these assumptions. The use of models which neglect the intracellular delay before virion production can lead to severe underestimates of R0 and, hence, to overly optimistic predictions of how efficacious treatment must be in order to prevent or eradicate the disease. These results are also of importance for attempts at estimating R0 from similar epidemiological data as there is a correspondence between within–host and between–host models. Estimates of the life span of infected cells obtained from viral load data collected during drug treatment studies also depend on the assumptions made in modelling the virus life cycle. The use of more realistic descriptions of the life cycle is seen to increase estimates of infected cell life span, in addition to providing a new explanation for the shoulder phase seen during drug treatment. This study highlights the limitations of what can be learnt by fitting mathematical models to infectious disease data without detailed independent knowledge of the life cycle of the infectious agent.