I've found some theory about various type of terminations but I can't figure in which cases are used parallel(pullup with half driving voltage and pulldowns) and thevenin termination. Since I'm used to simply boards with microcontrollers, where I can encounter this two type of termination and in which cases? Are something used in "extreme" cases like very long cables, critical or high power EMI applications?
Proper termination is needed at the beginning and end of a transmission line.
If the termination is not there or has the wrong impedance, the signal you're trying to transport will reflect and distort. This becomes an issue when the length of the transmission line is longer than the wavelength of the signal.
Termination is not always of the Thevenin variant. It depends what the next circuit, which is receiving the signal, needs. If that is a simple inverter then a DC voltage of 0 V (ground level) will not make it work. Inverters need around half the supply voltage to act as an amplifier. This is where the Thevenin termination comes in. It terminates the transmission line but at the same time provides the proper DC biasing voltage for the next stage.
Since you are talking about microcontrollers, I'm only addressing logic pulses here. For these kinds of pulses you can singly terminate. Let's assume the transmission line is 50 Ohms. If a 50 Ohm resistor to ground was placed at the receiving end the line would be properly terminated. The problem is when the send end was high, the current needed to maintain this level would be Voh/50, which is hard even on buffer chips. By switching to at 100 Ohm up and 100 Ohm down Thevenin terminator, the high state the current is reduced to (Voh-Vth)/50. It is much easier to find drivers to do this. Another way to terminate is to put the 50 Ohm resistor in series at the transmitting end. Series termination is the lowest demand on the driver. The way it works is on the edge of the pulse the signal is cut in half at the send end. When it arrives at the receiving unterminated end, it will double providing the original pulse. In this case the current seen by the driver is just the receiving gate Iil or Iih. In series termination there will be a step in the pulse for the round trip delay but this distortion doesn't matter.
Open collectors are current sources with a pull-up are like voltage sources with a series R.
But more often drivers are lower than Zo so series R's need to be considered if not built in. You examine this by the incremental V/I specs like Vol/Iol and (Vcc-Von)/Ioh vs temp and Vcc.
When threshold is critical for noise , terminate with an active DC bias to threshold or use two R's to make the equivalent bias to improve margin to binary errors from noise so that the margin is equal for each polarity. Matching the impedances from source to line to load help reduce ringing caused by mismatch.
To determine when to apply these rules you consider if the propagation delay is greater than the rise time. Then you must apply.