Speech is pretty well understood - there are two complementary aspects to it, speech production (synthesis) and speech recognition (via the changing frequency components as show up in the spectrogram).
When we recognize speech is almost as if we're hearing the way the speaker is articulating words, since what we're recognizing is the changing resonant frequencies ("formants") of the vocal tract corresponding to articulation, as well as other articulation clues such as the sudden energy onset of plosives or high frequencies of fricatives (see my other post in this topic for a bit more info).
High quality (that is, highly intelligible) speech synthesis has been available for a long time based on this understanding of speech production/recognition. One of the earliest speech synthesizers was the DECTalk (from Digital Equipment) introduced in 1984 - a formant-based synthesizer based on the work of linguist Denis Klatt.
The fact that most of the information in speech comes from the formants can be proved by generating synthetic formant-only speech just consisting of sine waves at the changing formant frequencies. It doesn't sound at all natural, but nonetheless very easy to recognize.
The starting point for human speech recognition is similar to a spectrogram - it's a frequency analysis (cf FFT) done by the ear via the varying length hairs in the inner ear vibrating according to the frequencies present, therefore picking up the dominant formant frequencies.