I have understood that logs are useless except for turning them to planks. If so, then how come my storehouses are full of logs, my sawmills says 0% and for sure I have saws in my sawmills. What's the missing link here? Does the game try to turn any logs I have into planks or do I have to tell it somehow?

I assume that you speak about Settlers 2.
Yes, the logs are just there to be turned into planks. However if your sawmills are not working, then doublecheck whether they are occupied, whether the building's production is not stopped (white flag-like symbol with red cross near the doors) and most importantly whether you have built road to the sawmill.