Museums cannot use photos, videos or other materials that they have collected, without the written permission of the person who created the photo or video. And: without the written permission of the person(s) who can be seen in a photo, video or other artwork.
The copyright law protects the person who made a photo, video or other artwork. You cannot publish anything, without the explicit, written permission of the creator of that item or whoever has the copyright of that item.
There are exceptions, for instance for materials that are in the 'public domain'. Anything that is in the public domain, can be used without permission.
You may also be able to use old materials: 70 years (but the number of years is different in some countries) after the maker of a photo or video dies, the material becomes part of the public domain and can be used without permission.
An ongoing debate is whether 'embedding' a photo or video in an online exhibition is a breach of copyrigh law. The European Court of Justice ruled that embedding (legal: framing) content on other sites is generally not relevant under copyright law. It is instead comparable to a link. This means that any public material (photos, videos) can be re-used on another website - if the original work has been published openly and is accessible to all internet users with the copyright holder’s permission (see: Europeana).
Orphan works are creative works or performances that are subject to copyright - like a diary, photograph, film or piece of music - for which one or more of the right holders is either unknown or cannot be found.
Personal Data Protection (GDPR)
The General Data Protection Regulation (GDPR) is an EU-wide regulation that controls how companies and other organizations handle personal data.
The GDPR protects the people that are IN a photo, video, or other artwork. If an individual in a photo or video can be recognized or identified, the photo or video is considered to be personal data. You are not allowed to use these materials publicly, without the explicit written permission of the persons who are visible in that photo, video or other artefact.