I am a freelance translator, and once received a request from a client saying that they were supposed to translate a chapter of a book, but had to outsource this task as it was difficult. I declined this request, but assuming that the client was to translate the chapter so it could be published, how would authorship and copyright work? Can I expect to receive credit and royalties from the publication? If not, does the client take all of the credit and the royalties?
Copyright works somewhat differently depending on jurisdiction, and we can't give legal advice here, but this is a rough summary of how it tends to work:
If someone translates a copyrighted work, the translation has its own copyright which belongs to the translator. However, because the translation is a derivative work of the original, the copyright holder has the right to control (as in forbid or license) the publication and other exploitation of the translation. They do not automatically own the rights to the translation, but the translator cannot exploit their work unless the copyright holder of the original grants license.
If a translation is exploited, it is possible to receive royalties as a translator, but the details would have to be part of either the license agreement or the translator's contract with the publisher. In most cases translators do not receive royalties but a fixed remuneration for their translation service, because...
...It is also possible for a translator to create a translation as a work for hire. In this case the contract for the translation stipulates that the copyright for the translation belongs to its commissioner in return for the agreed upon remuneration. This tends to be the more common case.