Is there any application for iPhone to spy on my spouse's text messages?
Hmmm is if really necessary to track and spy on your partner's messages and emails? Why not be up front and ask him? Here's a link of the best apps in the market, anyway: http://spyonandroid.over-blog.com/best-android-spy-software-to-catch-cheating-spouse.html
You can try mspy.com - allows you to track Sms, calls, WhatsApp, tinder, geolocation etc.
Is this compatible with iPhone? I'm an iPhone user. Do I have to download this on the person's phone to track?