Double tax conventions
Japan has multiple double tax conventions with other countries principally for the elimination of double taxation and the prevention of tax evasion and avoidance.
These are intricate and complex documents. Broadly speaking, they include criteria to determine which country has primary taxation rights over an individual (or entity) who would otherwise be taxed twice on the same income, and then mechanisms to eliminate or reduce the burden of being doubly taxed. If an individual's centre of interest is determined as Japan (as is likely, but not a certainty, for the intended readership of this wiki), then Japan is likely to have primary taxation rights, and the individual may be able to reclaim taxes already paid to the other country. But this is not a given, and even if Japan is deemed the centre of interest, there might be certain income sources where the double tax convention gives primary taxation rights to the other country, or provides no mechanism for the elimination of double tax.
Your local Japanese tax office can supply a bilingual certificate of residency (PDF) for the purposes of claiming double tax convention benefits.
Country-specific information
Further detail on the Japan-UK Double Tax Convention can be found at United Kingdom#Japan-UK Double Tax Convention.
Credits
Many thanks to the following RetireWiki.jp users for writing this article: