This paper proposes an analysis of the syntax and semantics of complex cardinal numerals, which involve multiplication (two hundred) and/or addition (twenty-three). It is proposed that simplex cardinals have the semantic type of modifiers (〈〈e, t〉, 〈e, t〉〉). Complex cardinals are composed linguistically, using standard syntax (complementation, coordination) and standard principles of semantic composition. This analysis is supported by syntactic evidence (such as Case assignment) and semantic evidence (such as internal composition of complex cardinals). We present several alternative syntactic analyses of cardinals, and suggest that different languages may use different means to construct complex cardinals even though their lexical semantics remains the same. Further issues in the syntax of numerals (modified numerals and counting) are discussed and shown to be compatible with the proposed analysis of complex cardinals. Extra-linguistic constraints on the composition of complex cardinals are discussed and compared to similar restrictions in other domains.