Mobile phones may feature GPS (geo-location), multimedia capacity (photo, video and audio recording and sometimes transmitting), data processing and access to the internet.
Call and text data from mobile phones may be unencrypted, insecure and vulnerable to being tapped into by third parties in proximity to the mobile phone, using inexpensive equipment. Use an encrypted call and messaging application such as Signal (doesn't store meta data) or WhatsApp (make sure your version of WhatsApp is updated and note too that WhatsApp does store metadata).
Phones give out information about their location.
For example: As part of normal operation, every mobile phone automatically and regularly informs the phone service provider where it is at that moment. Many phones also have GPS functions, which can embed location information into other data such as photos, SMS messages and internet requests that are sent from the phone. Visit Am I being tracked? to check your phone!
Typically, the security of voice communication (and text messages) that travel through mobile phone networks is relatively weak. There are inexpensive techniques which third parties can use to intercept your written communications or to listen to your calls. If someone is in proximity to your phone, they can receive transmissions from it. (Check your Google history)
It is therefore vital to be aware of the information that is stored, both actively and passively, on your mobile phone.
As soon as possible, notify your mobile service provider that the phone has been lost or stolen to cancel its service.
Visit the websites of the apps that are installed on your phone. Search for an option to logout of other devices, revoke tokens, or de-register mobile devices. If no option exists, change your passwords for these sites immediately.
See: Password Managers (can be found under References).
The most effective action you can take to stop detection is preventative - see how to find a lost phone.
Install an Anti-Theft app, something like Avast Anti-Theft (Android only) will locate your missing/stolen device.
Never let people whom you don't trust get physical access to your phone; this makes it easy to install spy software.
If you are conducting private and important meetings, switch your phone off and remove the battery. Or don't carry the phone with you if you can leave it where it will be absolutely safe.
Make sure that any person with whom you communicate also employs the safeguards described here.
Don't forget that using a phone in public, or in places that you don't trust, makes you vulnerable to traditional eavesdropping techniques, or to having your phone stolen.