Although many proposals have been made concerning the truth conditions of conditionals, three have been clearly dominant in the literature: the material conditional account, Stalnaker's possible worlds semantics, and the non-propositional view.

Of these three semantics, the first was once the orthodoxy in philosophy. That is no longer the case, even if it still seems to be regarded as the “default” position by philosophers not actively working on conditionals, and it still has its proponents among philosophers who presently work on conditionals. Philosophers working on conditionals nowadays are more likely to favor a version of the non-propositional view, though most have their own specific semantics, which only they themselves adhere to, as a rule. (In this area of research, if one's semantics is not completely ignored by one's colleagues, it counts as a major achievement.)

In psychology, the situation is different in that relatively many psychologists working on conditionals, notably those working in the mental models tradition of Johnson-Laird [1983], are still inclined toward the material conditional account. By contrast, those working within the New Paradigm described in the previous chapter typically advocate some version of non-propositionalism. Stalnaker's semantics has never been popular as a semantics of indicative conditionals, either in philosophy or in psychology, but at least in philosophy many believe it to provide the best semantics of subjunctive conditionals.

In linguistics, again the situation is different. According to von Fintel [2011, Sects. 4, 5], there is hardly any support for non-propositionalism among linguists; instead, most linguists endorse the Lewis–Kratzer view. In this view, there is no such thing as a conditional operator; rather, antecedent clauses attach to overt or covert operators, restricting the domain of quantification of those operators. The Lewis–Kratzer view has not received much attention from either philosophers or psychologists.

All three main semantics of conditionals are known to have their virtues. However, all three also face severe problems. This chapter discusses these semantics and their virtues and problems.