nickmcummins - it does not require root
- it does not require a wired connection
- it does not require to be on the same network as the device accessing it
- it is free
- it supports not only remote screen access, but also many other features, including transferring files between your Android and the remote computer
Some notable disadvantages are:
- it appears to no longer support USB connections
- depending on the quality of the network, performance and quality will vary greatly
- sound cannot be played remotely
- reliability, responsiveness and frequency of disconnection
