The current state-of-the art is pretty ad-hoc, a lot of algorithms are applied together in order to get a good performance and most of them require carefully hand-crafted parameters in order to operate reliably in noise.
The main idea of most VADs is that we track and suppress noise first, then we apply some classifier to decide if the frame is speech or not and then we might want to apply some hangover to select significant speech regions and ignore small random variations in decision.
Few core ideas used are:
VAD operates in spectral instead of time domain, noise tracking is performed in mel bands.
Statistical-based noise removal method is applied in order to separate signal from stationary noise:
If there are multiple microphones, microphone-array signal separation can be used to find out signal sources and space and separate noise from speech using spatial properties.
GMM and other machine-trained classifiers are used for several features like pitch, signal levels and so on. Recent research includes recurrent neural networks for example:
Most of the VAD methods deal with stationary or almost-stationary noise and there is a great variety of tweaks you can apply here. For example you can replace simple Wiener noise suppression filter with IMCRA one and get a new noise suppression algorithm and, consequently, new VAD algorithm. Same way, you can replace the classifier or add a new features to it and it will give you a new algorithm. And every new parameter in the algorithms will need tuning, in particular tuning of the computational expenses.
This ends into fusion of the various systems, like the one available here:
One of the modern fast VADs available in public is VAD from WebRTC codec, it incorporates almost all the features existing:
and it's pretty reliable.
The major issue with VAD is that speech signal is considered alone and the methods for arbitrary audio signal recognition are in a pretty initial stage. So you can't distinguish speech from other sounds because you don't know what other sounds are. Also, the theory of separation of overlapped signals is also in a very initial stage. So most of the modern VADs operate on stationary noise only and can not deal with complex noises and overlapped speech. Things like bird singing in the background can make things pretty complex.