Not your actual browser history, no. That list lives on your device. But whoever controls the router can often see a log of the sites (domains) your devices visited, and that can look a lot like a history.
Who can see what
The router owner or admin can check the router's logs or a parental control dashboard. Many home routers and mesh systems show a per-device list of domains contacted, with timestamps. This comes from unencrypted DNS lookups and from the site name your browser sends when it opens an HTTPS connection, which the Center for Democracy and Technology notes still travels in plain text on most sites. They won't see full URLs, search terms or page content on HTTPS sites.
Other people connected to the same Wi-Fi (a roommate, a guest) can't see your traffic by default. They would need to deliberately run an interception attack, which is uncommon on a home network and still wouldn't break HTTPS.
Someone holding your phone or laptop while it's open is the bigger exposure. They can open your browser history directly, no network tricks required.
Closing the gaps
- Turn on encrypted DNS. Firefox's DNS over HTTPS hides lookups from others on the network, and Android has a Private DNS setting that does the same system-wide.
- Use a VPN to hide the domain list entirely; the router then logs only a connection to the VPN server.
- Lock your phone and laptop, and use private browsing if others share the device.
One caveat: if the Wi-Fi belongs to an employer or school, they may install monitoring software or certificates on managed devices, which can reveal far more than a router log. On your own personal device, that's not the case.