Given this is the same technology as used by computers I might be able to contribute this.
Modern laptops charge very quickly to 80% and then slowly for the last 20% as this is where it places stress on the battery wears them faster if you continue to blast them.
The charging electronics are monitored to boost the rate up to 80% (along with other factors such as temperature and age) and then more gradually. Some of the new systems are over-provisioned allowing a few blocks at a time to be relaxed or cycled for a period to benefit long term reliability.
As we have seen with the recent laptops and tablet/phones the efficiency of these devices is improving as much from the control and charging capabilities as the actual storage.
It's ironic that lead/acid batteries provide the charge regime you are familiar with of their own accord without any external charge monitoring other than holding a constant (absorb) charge voltage. This because all charge and discharge can only take place at the plate/electrolyte interface, allied to a finite time for the chemical changes to become uniform within the depth of the plates as charge or discharge is chemically absorbed or depleted. As this chemical change process naturally becomes less vigourous as the battery approches full state of charge, so it's charge current demands tail off.
I believe Li-ion batteries are not so different in respect of them making their own charge current demands, but as they can accomodate much higher charge rates some extra monitoring is necessary in the charge process for both safety and longevity.
BTW it seems new smartphones are benefitting from improved processor efficiency as much as charge regimes. My new XiaomI manages with a smaller capacity battery than its predecessor, and that's the reason given.
