LogMeIn is a remote access tool that allows you to connect from one device to another, acting as though you are sitting in front of the remote device. LogMeIn needs to be installed on the devices you wish to remotely control, and then those devices are accessed through a Web browser or app. LogMeIn requires a subscription, although there is a free trial period.
When you connect remotely to a machine, you see your desktop or you can work through a menu-driven interface instead for tasks like file transfers. We used LogMeIn several ways. We started by installing LogMeIn on a Windows machine in our office, then accessed it through the LogMeIn Web site from our iPad and MacBook Pro while traveling. We also used our iPhone to access the remote Windows machine. Then we switched roles and accessed our MacBook Pro from our iPad. In all cases, LogMeIn worked flawlessly, although it was very dependent on access speed (which is not surprising). We could retrieve files remotely, and put files from our remote device onto our home or office computers. We could also start our desktop using the WakeOnLAN capability (not all machines support this). There's full support for multiple screens, pointers and mice, and many other features.
We've used LogMeIn for over a year, accessing our desktop from around the world on just about every type of mobile device you can think of. As long as there's a Web browser, you can touch your remote device. While there are a few competitors in this niche, LogMeIn is the one we've been using and will keep using because it has never failed us.