1. Core Legal Answer & Context: Codification in international law refers to the process of systematizing and formalizing existing customary international law, or developing new rules, into written treaties or conventions. The 20th century witnessed significant efforts towards codification, driven by the desire for greater certainty, clarity, and universality in international relations, especially after two World Wars. Early attempts under the League of Nations, such as the 1930 Hague Codification Conference, had limited success but laid groundwork.

The primary impetus for codification in the 20th century came with the establishment of the United Nations. Article 13(1)(a) of the UN Charter explicitly mandates the General Assembly to 'encourage the progressive development of international law and its codification.' To fulfill this, the UN established the International Law Commission (ILC) in 1947. The ILC, composed of legal experts, plays a crucial role by preparing draft articles on various topics, which are then submitted to the General Assembly. These drafts often form the basis for multilateral treaties adopted by states.

Major achievements in codification during the 20th century include:

• Law of Treaties: The Vienna Convention on the Law of Treaties (VCLT, 1969), largely based on ILC drafts, codified fundamental rules governing treaties.
• Law of the Sea: The four Geneva Conventions on the Law of the Sea (1958) and later the comprehensive United Nations Convention on the Law of the Sea (UNCLOS, 1982) codified vast areas of maritime law.
• Diplomatic and Consular Relations: The Vienna Convention on Diplomatic Relations (1961) and the Vienna Convention on Consular Relations (1963) standardized practices in these fields.
• International Criminal Law: While the Rome Statute of the International Criminal Court (1998) came at the very end of the century, it represents a monumental codification of core international crimes (genocide, crimes against humanity, war crimes, aggression).
• Human Rights Law: A series of conventions, including the International Covenant on Civil and Political Rights (ICCPR, 1966) and the International Covenant on Economic, Social and Cultural Rights (ICESCR, 1966), codified human rights principles.
• State Responsibility: The ILC's Articles on Responsibility of States for Internationally Wrongful Acts (2001), though not yet a treaty, are highly influential and reflect customary law.

Challenges to codification included state sovereignty, diverse legal traditions, and political disagreements, but the overall progress significantly enhanced the predictability and rule of law in international affairs.

2. Relevant Statutes and Sections:

• UN Charter, Article 13(1)(a): Mandates the UN General Assembly to initiate studies and make recommendations for the purpose of 'encouraging the progressive development of international law and its codification.'
• Statute of the International Law Commission (1947): Defines the ILC's functions, distinguishing between 'progressive development' (creating new law) and 'codification' (systematizing existing law).

3. Important Landmark Cases:

• North Sea Continental Shelf Cases (ICJ, 1969): The International Court of Justice examined the relationship between treaty provisions (codification efforts) and customary international law, clarifying how treaties can reflect, crystallize, or generate new customary rules.
• Military and Paramilitary Activities in and against Nicaragua (Nicaragua v. United States) (ICJ, 1986): The ICJ affirmed the parallel existence of customary international law and treaty law, even when their content is identical, reinforcing the idea that codification does not necessarily extinguish the customary nature of a rule.

4. Clear Conclusion: The 20th century marked a transformative era for international law, largely due to systematic codification efforts spearheaded by the United Nations and its International Law Commission. These endeavors, resulting in numerous foundational treaties, brought unprecedented clarity and structure to various domains of international relations, moving international law from a largely customary system to one increasingly governed by written norms, despite inherent political and legal complexities.