My impression is that a smartphone has no physical shutter. Rather, it admits light to the sensor's photo-sites under the control of some on-and-off, or perhaps read-twice-and-subtract, electronic method. 

Is that that generally accurate?  If so, could someone point me to a beginner-level description of how it works?

If the operation is electronic, does that mean there's no inherent fastest or slowest "shutter speed" for a given smartphone?