We have analyzed and extended the concept of fragility introduced by Angell. Although they often appear to be correlated, we have separated the property of "strength" from that of "fragility." We have taken the measure of "strength" to be the activation free energy at constant density, E-infinity(rho), for relaxation processes at relatively high temperatures; strong liquids, those with E-infinity(rho) much greater than kT over the relevant temperature range, relax via activated processes, whereas weak liquids do not. As the measure of "fragility" we have taken the curvature of the effective activation energy determined at temperatures well below the melting point where relaxation for all but the most nonfragile liquids appear to be activated. We have discussed a number of examples including weak-fragile and weak-nonfragile systems. We have suggested how these indicators of dynamical behavior might be correlated with thermodynamic indicators (entropy) and structural indicators (intermolecular interactions, structural frustration, collective interactions) as well as with other dynamical indicators such as the degree of nonexponentiality in the relaxation. We have also discussed the limitations of scaling data about the glass-transition temperature, T-g.