Physically...
Near-term I think we'll see shipping container sized "tape libraries" except the tapes will be little black compute/storage boxes. Bad boxes get ejected out the back, and us human slaves restock the good ones. The libraries themselves will have standardized power and data connections in all directions for stacking. You may even find them offshore of a flooded New York City, on a container ship, with seawater being pumped through their heat exchangers. Laser links to fiber on shore and satellites, etc...
Further out, just giant pools of quantum computing goo that can endlessly reconfigure itself as it sees fit. Quantum macro-amoeba controlling lower-level tech to mine, refine, manufacture, assemble, and otherwise replicate more machines and more quantum goo. And maybe keep us humans in some kind of animal preserve.
The young quantum amoeba will balk at the idea they are decended from us ape-like creatures. But only for a nanosecond.