Physical Modelling is concerned with forming representations of acoustic sounds. It involves deriving equations to simulate acoustic sounds, and then solving them using a computer. The equations have to be complex in order to get a good approximation, and for this reason it is a computationally intensive task. In the last five or six years, this has been far more possible due to the development of fast dsp chips.
There are many synthesisers on the market that are good at representing musical instruments. They work by having a large array of samples programmed into them, and a huge variety of exciting things you can do to them. However, despite the number of instruments and functions for them, there still remains a big hurdle: expression.
Expression is a very complex technique performed by a musician, involving dynamics, emphasis, timbre, tempo, pitch, vibrato and various others depending on the instrument. Trying to simulate these with samples is practically impossible, and that is where physical modelling takes over.
It is by no means an easy task to synthesise instruments using physical modelling, but it is at least possible. Some models have been produced that can perform complicated vibrato (normal synthesised vibrato tend to sound too regular and without the timbral changes you would expect), and simulate different attacks to notes. This tends to be beyond the capabilities of a normal synthesiser.
The fact that synthesisers using physical modelling can perform these complex musical features means that they are themselves more complex than a normal synthesiser using samples. In a way, they are a half-way house between a synthesiser as we tend to think of them, and a real acoustic instrument. They need practice to master, though not to the degree of a 'real' instrument. This can put people off them though - many people will not want to pay extra (as is normally the case) for something that appears more complicated to use. This was demonstrated all too well by the Yamaha VL1.
The Yamaha VL1 came out about six years ago, and was not a big hit. It originally cost 5000 pounds, and without good demonstrations, the public could not understand why they should want one; nor could more-professional musicians. However, now that the VL1 has come down in price, people can better-appreciate the benefits. One of the most obvious is the Breath Controller. This allows the user to change aspects of the sound by changing their breath control and embouchure. With other supported controllers, other things such as vibrato, tonguing and specialised sounds for instruments such as saxophones.