So how to you control the content your kids access through their iPhone / iPod / iPad / Android / Blackberry / Windows Mobile / PS3 / PS4 / XBox 360 / XBox One / Wii / Wii U / Smart TV / laptop / desktop / etc?
You filter centrally at the Internet access source: the router/firewall. All the devices regardless of what they are need to go through that choke point, so let's capitalize.
Home-based routers come with some basic blocking tools for the most part, but since it implies you manually add sites one-by-one (augh), consider it pretty much useless.
How let's look at something much stronger, effective & free: OpenDNS. This service is based on DNS entries (or the Internet equivalent of the white pages which translates domain names like google.com to an IP address like 184.108.40.206). You need to open an account and you can use their parental controls, free, if you are a home user. They even have a service named Family Shield (again free) designed to block adult web sites. They also have a paid option for those who want support. You need to replace your ISP's DNS entries in your router with the OpenDNS ones (easy trust me) and they have guides for most brands.
Once you set this up you need to log on their web site to configure your preferences (what you want to block, blocking message, etc.) and you're off to the races. You also need their DNS updater software running on a PC/Mac which is "always on" as your ISP must give you a dynamic IP address (it changes on a regular basis) and OpenDNS identifies you with that IP address. You get this software here.
So what's the best method? Education, talk to your kids. Stuff found on the Internet is not always kids-friendly and you have to teach them that part before deploying stuff. Then you geek out and install something.
'hope this was useful - leave comments if you have questions and/or suggestions!