Thanks for the example of the transistor and the words.LED are usually modelled the same way other diodes are, so there is logarithmic dependance between voltage and current. Same goes for transistors and other things, all the basic components are modelled quite accurately. Trouble comes with other parts like general ICs, those are modeled using those primitive devices and can often be quite far from reality, or can cause extremely slow or not at all working simulations, but that is a problem in the model and not the simlator.
Look at what parameters can be definded for a simple NPN transistor for example here http://www.ece.uci.edu/docs/hspice/hspice_2001_2-102.html
Lots of components don´t have all the parameters entered, so the simulator just assumes some default. Opamps usually have fixed offset an input currents, but you should be able to modify those and try different values, also there are different classes of models of for example opamps, which differ in realism and computation complexity, some will even run happily without any power supply connected.