We review the important general dynamic and thermodynamic properties of structural glass-forming substances and classify them into 12 different categories. Our understanding of glass-forming substances is incomplete until all these properties have been explained. The dynamic properties considered include those relating to the high frequency fast relaxation, the Johari-Goldstein beta-relaxation, and the slow structural alpha-relaxation. Practically all the important relaxation and diffusion processes in the time region extending from 10(-13) to 10(6) s have been discussed. We show from experimental data that the properties in different categories bear some relations to each other. Some issues that impede progress of our understanding of the behavior of glass-forming substances are accentuated by formulating them as questions. Answers to these questions by future experimental and theoretical investigations will improve our understanding. Specific suggestions for future research efforts that can provide some answers to these questions are also made. Within the same property in each category, by examining a large number of glass-formers, a pattern of variation is found which correlates with the departure of the structural relaxation of the glass-former from exponential decay or the quantity, (1 - beta), where beta is the fractional exponent in the Kohlrausch expression, exp[-(t/tau)(beta)]. These patterns, as well as their correlations with (1 - beta), suggest that the salient dynamic properties (or phenomenology) of glass-forming substances are all governed by the non-exponential nature of the structural relaxation, i.e., the quantity (1 - beta). Therefore, a theory or model capable of relating the structural relaxation time tau to (1 - beta) has the potential of explaining many of the salient dynamic properties of glass-forming substances. (C) 2000 Elsevier Science B.V. All rights reserved.