A non-transitory machine-readable storage medium encoded with instructions executable by a processor of a local computing device (100, 300), the storage medium comprising: instructions to provide, to a remote computing device over a network interface of the local computing device (100, 300), composite display information useable by the remote computing device to display a remote display area including a plurality of input lenses (211, 212, 213, 311, 312, 313) each depicting a respective region of a graphical user interface (142, 170) displayed by the local computing device (100, 300); instructions to, for any particular one of the input lenses (211, 212, 213, 311, 312, 313), change which region of the GUI (142, 170) is depicted in the particular input lens (211, 212, 213, 311, 312, 313) without changing which region of the GUI (142, 170) is depicted in any other input lens (211, 212, 213, 311, 312, 313); characterized in that in response to receiving, from the remote computing device, an input focus command identifying a first input lens of the plurality of input lenses, give input focus to the first input lens that displays a first region of the GUI displayed by the local computing device; render a second input lens, that displays a different second region of the GUI displayed by the local computing device and which is on top of the first input lens, with a partial transparency based on the first input lens having the input focus, and in response to receiving, from the remote computing device, another input focus command identifying the second input lens, render the second input lens with a second transparency based on the second input lens having the input focus, wherein the second transparency is less transparent than the partial transparency; and instructions to, in response to detection of a GUI input event (254, 256, 258, 259) with the remote computing device within any given one of the displayed input lenses (211, 212, 213, 311, 312, 313), when the given input lens (211, 212, 213, 311, 312, 313) has input focus, invoke the GUI input event (254, 256, 258, 259) at the local computing device within the region of the GUI depicted in the given input lens (211, 212, 213, 311, 312, 313). instructions to provide, to a remote computing device over a network interface of the local computing device (100, 300), composite display information useable by the remote computing device to display a remote display area including a plurality of input lenses (211, 212, 213, 311, 312, 313) each depicting a respective region of a graphical user interface (142, 170) displayed by the local computing device (100, 300); instructions to, for any particular one of the input lenses (211, 212, 213, 311, 312, 313), change which region of the GUI (142, 170) is depicted in the particular input lens (211, 212, 213, 311, 312, 313) without changing which region of the GUI (142, 170) is depicted in any other input lens (211, 212, 213, 311, 312, 313); characterized in that in response to receiving, from the remote computing device, an input focus command identifying a first input lens of the plurality of input lenses, give input focus to the first input lens that displays a first region of the GUI displayed by the local computing device; render a second input lens, that displays a different second region of the GUI displayed by the local computing device and which is on top of the first input lens, with a partial transparency based on the first input lens having the input focus, and in response to receiving, from the remote computing device, another input focus command identifying the second input lens, render the second input lens with a second transparency based on the second input lens having the input focus, wherein the second transparency is less transparent than the partial transparency; and instructions to, in response to detection of a GUI input event (254, 256, 258, 259) with the remote computing device within any given one of the displayed input lenses (211, 212, 213, 311, 312, 313), when the given input lens (211, 212, 213, 311, 312, 313) has input focus, invoke the GUI input event (254, 256, 258, 259) at the local computing device within the region of the GUI depicted in the given input lens (211, 212, 213, 311, 312, 313).