This review article covers major aspects of mathematical chemistry, QSAR, chemoinformatics, bioinformatics, and molecular modeling research carried out by Subhash C. Basak and coworkers during 1968 to the present time in three distinct phases: 1) Department of Biochemistry, University of Calcutta and Charuchandra College, India (1968-1981); 2) Department of Chemistry & Biochemistry, University of Minnesota, Duluth, USA (1982-1987), and 3) Natural Resources Research Institute, University of Minnesota, Duluth, UMD-NRRI (1988-date). Topics discussed include development of novel mathematical descriptors of molecules and biomolecules; QSAR, HiQSAR, DiffQSAR and I-QSAR studies using chemodescriptors and biodescriptors; formulation of arbitrary quantitative molecular similarity analysis (QMSA) and tailored QMSA methods and their applications. The role of proper statistical methods in QSAR formulation and validation as well as the critical role of such methods in the molecular descriptor landscape of the twenty first century are also addressed.