The sound must be shaped, in both amplitude and spectrum. To do this, the digital equivalents of Amplifiers and filters are used. These are controlled by other familiar items, Envelope Generators and Low Frequency Oscillators. The more esoteric processors such as Ring Modulators are rare, but do turn up occasionally. There is little computation involved in amplifiers, LFOs or envelopes, so the complexity offered is usually determined by the sophistication of the user interface or marketing considerations.
Filters are another story.
Analog filters hung on in synthesizers long after everything else had become digital. That is because a digital filter is computationally complex, and programming them was not well understood. That has changed. Recent models have very clean and flexible filters ranging from simple low pass to the 14 pole morphing filters found in the UltraProteous. Complex filters are usually implemented in a second processor, and require a large section of memory, so they do run up the cost of a machine, but as with analog synths, a good filter can make up for a lot of deficiencies in the sound generator.