 The concept of “general model” was introduced by Henkin (1950) in order to obtain a Completeness Theorem for second-order logic. General models are not the intended models of the axioms in the sense that bound relation and function variables do not range in these models over all relations and functions, only over a collection of them. The generally accepted attitude towards them is that they are not what one wants but they are necessary for obtaining a smooth theory. They are like irrational numbers in calculus: it would be ideal if all lengths that we encounter in calculus (or geometry) were commensurable, but that is not how things turned out. Some lengths are incommensurable, and we end up accepting irrational numbers in order to have a smooth general theory of lengths and their proportions. General models can be also compared to transitive models of set theory. One transitive model may say one thing is true, another says just the opposite is true. But together the transitive models help us understand the axioms of set theory. The current methods in the metamathematical investigation of the axioms of set theory, namely inner models and forcing extensions, all use transitive models of set theory in an essential way. Similarly general models of second-order logic help us investigate metamathematical properties of second-order logic and its axioms.