Core Legal Answer & Context: The relationship between international law and municipal (domestic) law is a foundational theoretical debate, primarily addressed by dualism and monism, with many states adopting a more pragmatic, mixed approach.

1. Dualism: Views international law and municipal law as two entirely separate and distinct legal systems. For international law to apply domestically, it must be 'transformed' or 'incorporated' into municipal law through specific legislative acts. Without such an act, international law has no direct effect within the domestic sphere. Conflicts are avoided because they operate in different spheres.
2. Monism: Views international law and municipal law as part of a single, unified legal system. International law is considered supreme and automatically applicable within the domestic legal order, without the need for transformation. In case of conflict, international law prevails over municipal law.
3. Harmonization/Coordination (Modern Approach): Many states, including India, adopt a nuanced approach. They recognize the distinct nature of the two systems but seek to achieve a degree of harmony. International law is often used as an aid to interpret ambiguous domestic statutes, and some international norms (especially customary law or human rights treaties) may be directly applicable or incorporated through judicial pronouncements, even without specific legislation.

Relevant Statutes and Sections:

1. Article 51 of the Indian Constitution (Directive Principle): States that the State shall endeavour to foster respect for international law and treaty obligations.
2. Article 253 of the Indian Constitution: Empowers Parliament to make any law for implementing any treaty, agreement, or convention, indicating a need for legislative action for treaties to have domestic effect.

Important Landmark Cases:

1. Kesavananda Bharati v. State of Kerala (1973): The Supreme Court held that in case of ambiguity, municipal law should be interpreted in a manner consistent with international law.
2. Vishaka v. State of Rajasthan (1997): The Supreme Court held that international conventions and norms, unless contrary to domestic law, can be used to interpret fundamental rights and fill legislative gaps, effectively incorporating them into domestic law in certain areas.

Clear Conclusion: While dualism and monism offer theoretical frameworks, most states adopt a pragmatic, mixed approach. International law increasingly influences municipal law, particularly in human rights, but its direct applicability often depends on constitutional provisions, legislative action, and judicial interpretation, aiming for a coordinated rather than strictly hierarchical relationship.