Connect a bluetooth keyboard and mouse to a smartphone, add a video connection (possibly via a dock, at least initially to reduce price), make application UIs reasonably scalable or adopt two separate UIs - one for the little screen and one for the big screen, and there we go.
Storage is not a big concern for these things - SD cards are available in capacities of 64 GB and more, DRAM is also reasonably cheap, so that isn't a problem (and if it is, I think it would go away simply by allowing bulky external storage like USB drives to be attached). Batteries are still not very adapted to such demanding uses but it looks like the "energy crisis" is a constant companion of our civilization so we'll just live with it until some exotic energy sources are developed.
We have decent Internet connectivity already - data can be securely replicated (NOT stored in the cloud) where and when it's needed, and the technological future looks bright.
Of course, taking these ideas to extremes, with continued miniaturization (which may or may not be possible), we can linearly predict a really SF-like future, with smartphones with features like these migrating inside people. But there is still much to go before that starts happening.