controlling over wi-fi

I am new to Arduino and looking to control a device over wi-fi, with let's say an iphone or a web browser. i have been googling alot and from what I understand, the easiest proposed solution is to hook an arduino to ethernet/wifi and relay commands to other arduinos via RF or other means. This is good for indoor applications, but what about outdoor or if there is no wifi network ?

I found this remote controlled drone : "The Parrot AR.Drone generates its own Wi-Fi network to which you connect your iPod touch or iPhone to control. The front camera view is streamed to your piloting device display."

Is it possible with an arduino and what kind of setup would you need ? The drone is sold 300USD, so I guess it wouldn't be a cheap solution.

Thank you for your time. Philippe

This guy used an old Linksys router to do what you want:

I was thinking of something smaller, that could fit in a light bulb for example. Not sure it is possible, that's why I am asking here.

Well, a full size Arduino won't wit in a lightbulb so that leaves out regular WiFi shields. There is a device called the "Yellow Jacket". It appears to be an Arduino Nano with built-in WiFi. Unfortunately it appears to be out of stock right now.

You can get just the SPI/WiFi part for $29:

Great ! This is more something like this I was looking for ;))) Thank you

I am a web developper, components and electricity are not my field of expertise, I bought an arduino kit to start learning and ideas pop out my head now.

In fact, looking at this appliance :

I thought that If it had its own wifi network, you could connect directly to it and use a web application run by an arduino to control it, and even get rid of the remote. I am thinking of something very simple, that anyone could connect to easily.

Do you think it is feasible, or is it fantasy :P ?

Regards, Philippe