Models-and-modeling perspective (MMP) is a problem-solving and learning perspective in mathematics education. Although modeling processes have been addressed widely in the international discussion on mathematical modeling, a homogeneous understanding has not been established yet. Hence, the field needs studies addressing the epistemological grounds of model development. Therefore, in this study, I aimed to scrutinize the latent aspects of modeling in MMP-based research. Based on the analysis of 143 chapter-sized documents, I aimed to articulate the characteristics of the modeling process and the models. The thematic analysis that was incorporated in document analysis revealed four latent aspects, namely, modeling: (1) is a subjective and also inter- and intra-subjective process; (2) encompasses both structural and systematic properties; (3) produces models that are both implicit and explicit to a certain degree; and (4) culminates in an incomplete -- but not inadequate -- model. These aspects of model development led me to reconceptualize what a model conveys in MMP-based research and articulate the potential and limits of the models. This is particularly important for teachers and researchers in understanding what models indicate in relation to students' ways of thinking, and such a systematic and analytical investigation can contribute to the scholarly conversation about modeling in the field of mathematics education.