Higher-order thinking is relational reasoning in which multiple representations are linked together, through inferences, comparisons, abstractions, and hierarchies. We examine the development of higher-order thinking in 64 preschool-aged children, observed from 14 to 58 months in naturalistic situations at home. We used children's spontaneous talk about and with relations (i.e., higher-order thinking talk, or HOTT) as a window onto their higher-order thinking skills. We find that "surface" HOTT, in which relations between representations are more immediate and easily perceptible, appears before--and is far more frequent than--"structure" HOTT, in which relations between representations are more abstract and less easy to perceive. Child-specific factors (including early vocabulary and gesture use, first-born status, and family income) predict differences in children's onset (i.e., age of acquisition) of HOTT and its trajectory of use across development. Although HOTT utterances tend to be longer and more syntactically complex than non-HOTT utterances, HOTT frequently appears in non-complex utterances, and a substantial proportion of children achieve complex utterance onset prior to the onset of HOTT. This finding suggests that complex language is neither necessary nor sufficient for HOTT to occur; other factors above and beyond complex linguistic skills are involved in the onset and use of higher-order thinking. Finally, we found that the trajectory of HOTT, particularly structure HOTT--but not complex utterances--during the preschool period predicts standardized outcome measures of inference and analogy skills in grade school, which underscores the crucial role that this kind of early talk plays for later outcomes. [This paper was published in "Cognition" v200 Article 10427 Jul 2020.]