Studying bitumen has always posed a challenge to researchers owing to its extreme complexity and unique properties. To classify it commercially and to determine bitumen grade, two standard empirical tests have been adopted within the European standardized bitumen binders system [EN 12591:2009 (2009) Bitumen and bituminous binders – Specifications for paving grade bitumens]: Softening Point (SP) and Penetration (PEN). The relationship between these two tests and the physical or chemical properties of bitumen is not well understood. For the first time, this study represents an attempt to build more understanding of such a relationship through a comprehensive study of the correlation between the two standard tests and many physical and chemical properties of bitumen. A second goal is to propose some predictive models for these two tests and compare their predictive accuracy. Therefore, 13 Straight Run Vacuum Residues (SRVR) samples from different geographical origins were analyzed to measure the following parameters: Dynamic Viscosity (VisDy), Conradson Carbon Residue (CCR), C5 Asphaltenes Content (AspC5), C7 Asphaltenes Content (AspC7), Elemental Analysis (including C, H, O, N, S, Ni, and V content), Simulated Distillation (SD), Fourier-Transform Infrared Spectroscopy (FT-IR), and proton nuclear magnetic resonance spectroscopy (H-NMR). Results of studying correlations using correlation matrix and Principal Component Analysis (PCA) have emphasized the prominent effect of asphaltenes content on the other properties and the results of SP and PEN. It has also shown the potential importance of the aliphaticity/aromaticity of bitumen. Then, four models were proposed for the prediction of SP and PEN: viscosity, FT-IR, H-NMR, and multi-parameter models. Partial least squares (PLS) regression was used for building all models, except viscosity ones. All SP models, except H-NMR model, exhibited very good accuracy compared to the standard method. On the other hand, PEN was more difficult to predict than SP and only the multi-parameter model of PEN showed relatively good accuracy of prediction.