Kant's mature teleological philosophy in the Critique of the Power of Judgment is predicated on innovations that address a set of unprecedented challenges arising from within critical philosophy. The challenges are (1) a threat of “transcendental chaos” between sensibility and understanding, emerging from the structure of critical epistemology; (2) a threat of “critical chaos” between determination and reflection, generated by Kant's response to that first threat. The innovations include (a) a transcendental conception of purposiveness, (b) a principle of nature's purposiveness based on that conception, (c) a power of judgment governed by that principle, (d) and so governed in an unusual (self-given and self-governing) way, (e) a view on which nature does make leaps. This Element argues that Kant's mature teleological philosophy – and a fortiori Kant's aesthetics and philosophy of biology – cannot be understood without a fully systematic account of these challenges and innovations, and it presents such an account.