Most of the stories involve Trurl and Klapaucius using their extraordinary technological abilities to help the inhabitants of the medieval planets, usually involving neutralizing tyrants. For example:
Trurl and Klapaucius come to a planet ruled by a king who loves hunting. He has already "conquered" all the most dangerous of predators, and now hires constructors (engineers) to make new, mighty robotic beasts for him to hunt. He has already executed all of the previous constructors who visited because they could not build beasts that would be challenging enough to hunt. When the two famous Constructors arrive, they are arrested and ordered to construct a worthy foe for the king within twelve days.
The two face a dilemma: if they make something that the king will kill, they will be executed by the mad king. But if the king himself is killed, then they will be executed, for the next king will be pressured to show his respect for the previous. They solve the problem by building an animal that survives the hunt (involving both cyber-hounds and nuclear tipped missiles unleashed upon it, in the characteristic cartoonish manner) and takes the king hostage by, nothing less, turning into several police officers and presenting an order for his arrest. All the king's men fail to find and free the king (partially because in searching for the fake policemen one half of the real police force arrests the other half), and he is released only after the Constructors' numerous demands are met.
On another occasion, Trurl and Klapaucius are captured by an interstellar "PHT" pirate. Trurl offers to build a machine capable of turning hydrogen into gold (something he can do manually, which he demonstrates by hand, mixing up protons and putting electrons around). However, the pirate turns out to have a PhD and cares not for the riches, but for knowledge (and in fact points out that gold becomes cheap if it is abundant). Trurl therefore makes a modified Maxwell's demon for him, an entity that looks at moving particles of gas and reads information that is, coincidentally, encoded in their random perturbations. This way, all the information in the universe becomes easily available. The demon prints out this information on a long paper tape, but before the pirate realizes most of the information is completely useless (although strictly factual) he is buried under the endless rolls of tape, ceasing to bother anyone.