A Wi-Fi network can show you which domains a device contacted, but not the search terms typed into a search engine — those live on the device or in the signed-in Google/Apple account, never in the router's traffic. Most people asking this want "what did the phone search for", and the accurate place to look is the phone, in this order.
1. Google My Activity. For any account signed into Chrome or Android, myactivity.google.com lists searches and page visits by date. It is free, first-party, and the fastest honest answer.
2. The browser's own history, if you can unlock the device. Safari history also syncs through iCloud when a family group shares an Apple Account.
3. The router's DNS log, only if logging is enabled. Log into the admin page (usually 192.168.1.1, credentials on the sticker), look for DNS, query or traffic logs. Expect bare hostnames and short retention, and expect gaps: browsers and phones increasingly use DNS-over-HTTPS, which bypasses the router's resolver entirely.
4. The ISP portal. Some providers expose per-device usage and connection logs to the account holder; none expose search queries. Bills never do.
For a child's line, the free first-party tools cover the legitimate version of this: Google Family Link activity reports and Chrome supervision on Android, Apple Screen Time web activity on iOS, and a filtering resolver such as OpenDNS FamilyShield at the router if you want network-level visibility without touching the phone.
Where Ultimate Phone Spy fits is the gap those leave on Android, Windows and Mac: web history, app usage and location in one dashboard for a device you administer (web history). It does not cover iPhone, because iOS blocks device-level access, and it is installed openly rather than remotely.
Pulling an adult's browsing history without their consent is a privacy-law exposure under GDPR and the Computer Misuse Act, not a clever network trick. We covered the bill myth in this thread.