Moral socialization of students consists of five elements: process, subject, agent, content and pattern. This paper discusses the studies of the former three: their progress and perplexities, covering the following puzzles: "Why does the youth socialization take longer time?" "Are there any critical periods in student socialization?" "How do we identify over-socialization?" "Is "Education is student-based" a scientific statement?" "How do we assess the contribution percentages of the four key agents of student socialization?"