My Acacia dining table starting to show some huge splits or cracks
There's generally greater success with making it a feature than trying to hide it.

Clamping it together and gluing will generally fail unless it's also rehydrated to the level it was made at first, and then kept that way. So if you live with the air you have, not going to fly unless you buy locally made furniture or avoid solid wood in preference to veneers over plywood or MDF.

While you can fill with wood, or leave it open (first putting in butterfly keys to try to limit further movement) one of the more visually appealing methods is to use a "crushed stone inlay" (sometimes the stone is really plastic, which, since the epoxy holding the stone in is plastic, is not that huge of a deal if you like the way it looks.) Simply using colored (often black) epoxy is anoter stylistic option.

Turquoise in mesquite cracks is probably the most common example of this. 



I also know woodworkers who fill voids or make features by casting pewter directly into wood (it melts at a low enough temperature that this works.)