The purpose of this literature review is to explicate the facets of mathematical problem solving taxonomies in relation to mathematical modeling. Subsequently, components and learning benefits of mathematical modeling are discussed. Examples of mathematical problems are embedded in the discussion and pragmatic applications to mathematical learning, are provided. Mathematical modeling is a chief focus of the problem types and their structural characteristics (e.g. multiple entry points, multiple processes and products, opportunity to mathematize, interest generating, and pre-college level thinking) are detailed so that readers can consider prospective by-products. Such by-products may be, but are not limited to positive affective outcomes, high propensity to positively influence creative process and product, and conceptual learning while making sense of mathematics.