Recently, the advance of OCT enables a detailed examination of the human retina in-vivo for clinical routine and experimental eye research. One of the structures inside the retina of immense scientific interest is the fovea, a small retinal pit located in the central region with extraordinary visual resolution. Today, only a few investigations captured foveal morphology based on a large subject group by a detailed analysis employing mathematical models. In this work, we develop a parametric model function to describe the shape of the human fovea. Starting with a detailed discussion on the history and present of fovea research, we define the requirements for a suitable model and derive a function which can represent a broad range of foveal shapes. The model is one-dimensional in its basic form and can only account for the shape of one particular section through a fovea. Therefore, we apply a radial fitting scheme in different directions which can capture a fovea in its full three-dimensional appearance. Highly relevant foveal characteristics, derived from the model, provide valuable descriptions to quantify the fovea and allow for a detailed analysis of different foveal shapes. To put the theoretical model into practice, we develop a numerical scheme to compute model parameters from retinal \ac{oct} scans and to reconstruct the shape of an entire fovea. For the sake of scientific reproducibility, this section includes implementation details, examples and a discussion of performance considerations. Finally, we present several studies which employed the fovea model successfully. A first feasibility study verifies that the parametric model is suitable for foveal shapes occurring in a large set of healthy human eyes. In a follow-up investigation, we analyse foveal characteristics occurring in healthy humans in detail. This analysis will concern with different aspects including, e.g. an investigation of the fovea's asymmetry, a gender comparison, a left versus right eye correlation and the computation of subjects with extreme foveal shapes. Furthermore, we will show how the model was used to support investigations unrelated to the direct quantification of the fovea itself. In these investigations we employed the model to compute anatomically correct regions of interest in an analysis of the OCB and the calculation of an average fovea for an optical simulation of light rays. We will conclude with currently unpublished data that shows the fovea modelling of hunting birds which have unusual, funnel-like foveal shapes.