Income earned across a border can be taxed by the country where it arises and by the country where the recipient lives. Treaties exist because both claims are legitimate under domestic law.
Where the double claim comes from
Most countries tax residents on worldwide income and non-residents on income sourced locally. Someone resident in one country earning in another falls under both rules.
Without coordination, the same income is taxed twice, which would make cross-border activity uneconomic. Treaties resolve the conflict bilaterally.
They do not create tax. A treaty limits or allocates existing taxing rights and cannot impose a charge that domestic law does not already provide for.
How residence is determined
An individual or company can be resident in two countries under their respective domestic tests. Treaties include tie-breaker rules to assign a single treaty residence.
For individuals these consider permanent home, personal and economic ties, habitual abode and nationality in sequence. The tests are applied in order until one resolves the question.
For companies the traditional test looked to the place of effective management, though more recent practice often refers the question to agreement between the two administrations.
What a permanent establishment triggers
A company is generally taxable on business profits only where it has a permanent establishment. That usually means a fixed place of business or a dependent agent concluding contracts.
Short-term activity, preparatory work and independent agents typically fall outside the definition. The threshold determines whether a country may tax at all.
Definitions have been tightened in several treaties to address arrangements that fragmented activity to stay below the threshold. Wording differs between treaties and continues to be updated.
How relief is actually delivered
Two main methods exist. Under exemption, the residence country does not tax income already taxable at source; under credit, it taxes the income but allows a deduction for foreign tax paid.
The credit is usually limited to the domestic tax on that income, so no refund arises where the foreign rate is higher. Excess foreign tax may be carried forward in some systems.
Treaties also cap withholding rates on dividends, interest and royalties. Claiming the reduced rate normally requires certification before payment.
Why the network is uneven
Treaties are negotiated bilaterally, so coverage depends entirely on which pairs of countries have concluded one. Many pairs have none.
Provisions have been added in recent years to deny benefits where arrangements were designed principally to obtain them. These anti-abuse measures apply across large parts of the network.
Treaty terms, domestic law and procedural requirements differ by jurisdiction and change over time, so entitlement is confirmed case by case rather than assumed.