Question asking plays a fundamental role in learning, and the cognitive development literature contains many studies of specific types of question-asking skills. However, little is known about the developmental course across different aspects of question asking, of which we explore: (a) the ability to ask questions that enable children to solve a specific problem, (b) the ability to ask questions that will increase general understanding about a topic, (c) the ability to recognize the relevance of information yielded by another person's answer to a question, and (d) children's general levels of curiosity. The current study includes four tasks assessing preschool through first-grade children's curiosity and performance on the three different types of question-asking tasks listed above. We observed significant development between kindergarten and first grade in children's question-asking and significant correlations among the different question-asking tasks. Children who generated more questions for problem solving were better at recognizing effective questions, and generating questions for learning was related to generating problem-solving questions. Both the ability to recognize effective questions and to generate questions for learning were positively correlated with our measure of children's curiosity. The results and implications are discussed for understanding the development of question-asking skills and the role of curiosity as a fundamental motivator of children's question asking.