How safe is it to share photos and videos over messaging apps?

Sending a photo feels private and fleeting, but a copy leaves your control the instant it lands on someone else's phone. Encryption protects a picture while it travels; it does nothing to stop the person at the other end from keeping it, forwarding it, or backing it up. Once you understand what you are really trusting, it is easy to share more carefully.

What you are actually trusting

The recipient. As soon as they have the image, they can save, screenshot, or forward it. No amount of encryption changes that.
Their phone and backups. Their device could be lost, shared, or backed up to a cloud that is not encrypted - and your photo goes with it.
Hidden data. Photos can carry details you cannot see, including where and when they were taken. Some apps strip this out, some do not.
"Disappearing" media. View-once and disappearing photos are a courtesy, not a guarantee - a second phone can photograph the screen, and screenshots happen.

Sharing more safely

Assume anything you send could be seen by someone else one day. If that thought makes you uneasy, that is your answer.
For anything sensitive, use an end-to-end encrypted app (Signal or WhatsApp), turn on view-once or disappearing media, and share only with people you trust. See how can I make Signal, WhatsApp and Telegram more private?
Strip location from your photos by turning off location tagging in your camera settings.
Be very wary of pressure. Sextortion - being pressured or threatened into sending intimate images, or blackmailed over them - is common. Anyone rushing or threatening you is running a scam, not a relationship. See how can I tell if a message is a scam?
With children, keep the message simple and repeat it: once an image is out, you cannot take it back.

If an image is already out there

If an intimate image of you is being shared or used to threaten you, stop engaging and do not pay - paying rarely ends it. Keep the evidence, report it to the platform, and use a free takedown service (StopNCII.org for adults, Take It Down for images of under-18s) that can help get it removed. Tell someone you trust; this is not something to carry alone.