Chromatography is the workhorse of biopharmaceutical downstream processing because it can selectively enrich a target product while removing impurities from complex feed streams. This is achieved by exploiting differences in molecular properties, such as size, charge and hydrophobicity (alone or in different combinations). Accordingly, many parameters must be tested during process development in order to maximize product purity and recovery, including resin and ligand types, conductivity, pH, gradient profiles, and the sequence of separation operations. The number of possible experimental conditions quickly becomes unmanageable. Although the range of suitable conditions can be narrowed based on experience, the time and cost of the work remain high even when using high-throughput laboratory automation. In contrast, chromatography modeling using inexpensive, parallelized computer hardware can provide expert knowledge, predicting conditions that achieve high purity and efficient recovery. The prediction of suitable conditions in silico reduces the number of empirical tests required and provides in-depth process understanding, which is recommended by regulatory authorities. In this article, we discuss the benefits and specific challenges of chromatography modeling. We describe the experimental characterization of chromatography devices and settings prior to modeling, such as the determination of column porosity. We also consider the challenges that must be overcome when models are set up and calibrated, including the cross-validation and verification of data-driven and hybrid (combined data-driven and mechanistic) models. This review will therefore support researchers intending to establish a chromatography modeling workflow in their laboratory.