 Three kinds of theory will be discussed. In §2 we compare truth-functional and non-truth-functional accounts of the truth conditions of conditionals. In §3 we examine what is called the suppositional theory: that conditional judgements essentially involve suppositions. On development, it appears to be incompatible with construing conditionals as statements with truth conditions. §4 looks at some responses from advocates of truth conditions. In §5 we consider the problem for the suppositional theory of complex sentences with conditional parts. In §6 we consider a wider variety of conditional speech acts and propositional attitudes.