The "plus" fraction of a petroleum fluid is a complex mixture that has long defied traditional chemical and thermodynamic treatments. This fraction of crude oil, by and large, cannot be analyzed. These fractions contain quantities identified as asphaltenes and resins that are solubility classes and, as such, are particularly difficult to characterize. Despite generations of study with ever-more-powerful scientific tools, the research community still has difficulty determining the physical and chemical properties of asphaltenes, and there is still no agreement regarding how these materials should be studied. To some extent, these difficulties may be inherent in the complexity of the petroleum fluids, but they have also been exacerbated by the acceptance of "conventional" wisdom. The "purists" at one end of the spectrum study only single-phase samples of live oil; however, experiments on such fluids samples are expensive and difficult, because of the typical high pressures that are encountered. At the opposite extreme are mechanistic studies that focus on isolated asphaltene fractions (model systems), where asphaltenes are precipitated from one source and then studied in a solvent completely different from the original crude oil from which they originated. Such research suffers from an imperfect model for asphaltenes in their natural environment. This paper will examine the successes and failures in applying scientific principles to asphaltenes and the flaw of assuming, either directly or tacitly, that asphaltenes and resins are a compound that has a structure that can be defined and has a separate identity that can be determined by isolating the class of compounds from their "native" state. New research that points a way forward is also discussed.