Into Futurity

Strange devices:

the Time Machine
the time projector
time corridors
T machines
the Dirac transmitter

(Wells, Anderson, Tipler and Blish.)

There are many such devices but this post focuses on these five and on the future, not the past.

Usually, fiction is set in its characters' present which can be the readers' past, future or alternative timeline. A narrative is set in its character's future if he time travels, e.g., with the Time Machine etc, or previews, e.g., with the Dirac transmitter. Thus, Wells' Time Traveler travels to 802,701 A.D., then to his "Further Vision," before returning to the nineteenth century when he tells his dinner guests about his passage through "tomorrow" and "into futurity."

The following works are eminently "Wellsian":

Poul Anderson's "Flight to Forever" (see "Flight to Forever" Timeline, Part I here and Part II here);
Anderson's The Corridors Of Time with its future periods of  the Wardens and Rangers, then of their successors, the time wardens;
Anderson's The Avatar (see jumps 1-4 here and 5-11 here);
James Blish's The Quincunx Of Time (see Chronology Of The Beep here).

Blish's characters see the future from the comfort of an office instead of traveling into it.