I use my phone on mobile data mostly, not the home WiFi. I always thought that meant my parents could not see what I look up. But my friend said their dad saw their history somehow and now I am not sure. Does mobile data actually hide your searches from parents or not?
Your mobile data traffic does not go through your home WiFi router, so your parents cannot see it from the router side. That part of what you assumed is correct.
But there is more to it. If your phone is on a family mobile plan, the carrier account holder (usually a parent) can log into the carrier website and see data usage. Not the actual URLs or search terms, but they can see how much data was used and sometimes which apps used it. That is a different thing from seeing search history.
Also your browser keeps history locally on the device. If a parent picks up your phone and opens Chrome or Safari, the history is sitting right there unless you cleared it. Mobile data does not wipe local history 
Can Parents See Your Searches on Mobile Data: The Real Answer
What Mobile Data Actually Does
When you use mobile data instead of home WiFi, your internet traffic goes through your carrier’s network instead of your home router. This means your home router logs nothing. Your parents cannot open the router admin page and see your searches.
What Parents Can Still See
The Device Itself
Browser history lives on the phone. Chrome, Safari, and most browsers save every visited page locally. That has nothing to do with WiFi or mobile data, it is just stored on the device.
Carrier Account Access
If your parents pay the phone bill, they have access to the carrier account. Most carriers show data usage per app and sometimes domain-level logs depending on the plan.
Monitoring Apps
If any parental monitoring app was installed on the device, it captures browsing data directly from the phone mobile data, WiFi, or offline activity. The network you are on does not matter at all in that case.
Bottom Line
Mobile data removes one visibility layer the home router. It does not remove the others.
SoloVibe covered it well technically let me add the part that most people skip over, DNS.
when you type a URL or do a search, your phone sends a DNS query first to translate the domain name into an IP address. on WiFi that query goes through your home router. on mobile data it goes through your carrier’s DNS servers instead. so yes, the home router sees nothing.
but here is the nerdy bit if your phone has a monitoring profile or VPN configuration installed by a parent or IT admin, DNS queries can be redirected to a logging server regardless of whether you are on WiFi or mobile data. this is how some parental tools work at a network level even outside the home. most parents do not do this but it is technically possible if someone set it up 
from a parent perspective I want to give the honest picture here 
most parents are not sitting there analyzing router logs or DNS queries. but the concern your friend had about their dad seeing history that most likely came from one of two places:
one the browser history on the actual device. super easy to find, no tech skills needed. just open the browser and tap the history icon.
two a monitoring app that was installed on the phone. apps like Xnspy run in the background and send browsing data to a parent dashboard. the parent does not need to touch the phone at all. they just log into the dashboard and see everything searches, sites visited, apps used regardless of whether you were on WiFi or mobile data when you browsed.
so mobile data is not the shield a lot of people think it is 
okay I want to address the friend’s situation PixelNode mentioned because that detail matters
if the dad saw history, one of two things happened. either the kid forgot to clear browser history and dad physically checked the phone. or there is a monitoring app on the device. those are basically the only two realistic explanations.
carrier logs showing actual URLs is pretty rare and usually requires the parent to specifically request detailed logs from the carrier which most do not bother with. so it is almost certainly one of the two simpler explanations above.
check your own phone go to Settings and look for any app you do not recognize or any profile installed under Settings > General > VPN and Device Management on iPhone. on Android check Settings > Device Admin Apps. if something suspicious shows up there, that is probably your answer
How Parental Monitoring Apps See Activity Regardless of Network
Why the Network Does Not Matter
Most people focus on WiFi vs mobile data when thinking about privacy. The thing is, a monitoring app installed on the device does not care which network you are using. It captures data at the application layer, meaning it sees what the browser sees before any network connection is even made.
What These Apps Actually Capture
Browser Activity
Apps like Xnspy log URLs and search terms from the browser directly. Private mode, mobile data, or WiFi none of that changes what the app can see because it is reading from the device, not the network.
App-Level Monitoring
Beyond browsing, these tools can also show which apps were opened and for how long. So even if you used an app instead of a browser for searches, activity gets logged.
How to Know If One Is Installed
On iPhone: Settings > General > VPN and Device Management. Look for any profiles you did not install yourself. On Android: Settings > Device Admin Apps or Battery settings monitoring apps sometimes appear there to stay active in the background.
I appreciate that TeraByte and FixTech gave both sides of this the tech side and the parent side
I am actually a parent and I will say this directly yes, parents can and do use monitoring apps. I used Xnspy on my kid’s phone starting when they were 13. not because I wanted to catch them doing something wrong, just because I wanted to know if something concerning was happening that they would not talk to me about. the app shows browsing history regardless of whether they are on mobile data or home WiFi.
I told my kid the app was there. some parents do not. but either way the app functions the same network type has no effect on what it reports. so the assumption that mobile data means invisible is not really how it works in practice 
adding a technical detail nobody has brought up which is HTTPS.
even on mobile data, all your searches through Google are sent over HTTPS which encrypts the content. so if someone was somehow watching your network traffic, they would see that you connected to google.com but they would not see what you actually searched. the query itself is encrypted.
HOWEVER and this is the part that gets people, the domain is still visible. so a network observer sees google.com, reddit.com, whatever site you visited. not the exact page or search term necessarily, but the destination. and as everyone above pointed out, a monitoring app on the device sees past all of that because it reads from the browser before encryption even kicks in 
real talk the question kind of answers itself when you think about it
if the phone belongs to your parents, or the plan is paid by your parents, then there is an argument that visibility into usage is part of the deal. a lot of parents see it that way. not saying it does not feel like a lot but that is kind of the reality for most teenagers.
the more useful question is probably less about hiding activity and more about understanding what your parents can actually see. VoterMobile gave good advice about checking for monitoring apps. if you find one, that opens a conversation worth having rather than a technical workaround to look for. speaking from experience as someone who was once 15 and also as someone who is now a parent
I want to circle back to what kodevortex said about VPN configurations because it is relevant and underexplained
some parents set up a managed MDM profile on the phone this is what schools do too on school devices. once that profile is installed it can route ALL traffic including mobile data through a monitored DNS or VPN endpoint. so even searches done on 5G can be logged if the device has that profile.
you can check for this on iPhone under Settings > General > VPN and Device Management. if there is a profile listed that you did not put there yourself, that is almost certainly a monitoring setup. at that point mobile data versus WiFi is completely irrelevant because the monitoring happens at the device level before traffic hits any network 
what mobile data protects you from: your home WiFi router logs. that is it. one layer.
what mobile data does NOT protect you from:
— browser history stored on the phone itself
— carrier account data summaries (no exact URLs usually but app-level usage)
— any monitoring app installed on the device, like Xnspy, which reads activity directly and sends it to a parent dashboard regardless of network
— MDM or VPN profiles that route traffic through a monitored server
— a parent just picking up your phone and opening the browser
the friend’s dad who saw history most likely either checked the browser directly or had a monitoring app running. ZenDelight confirmed from the parent side that apps like Xnspy work exactly that way.
so yeah, mobile data is one less thing but it is not really privacy 