The Zoid Core is the fundamental power source for all Zoids.
The techno-organic core that a Zoid is essentially formed around serves as its heart. Varying in appearance, the Zoid Core is not homogeneous for all Zoids. If a Zoid has it's Core damaged, it will die and cannot be repaired. Based on the Zoids: Chaotic Century and Zoids: New Century anime series', the Zoid's corpse will turn to stone after a while.
There are some exceptions to this, it has been seen that fusing with an Organoid can revive a Zoid even after its body has turned to stone. Furthermore, the Murasame Liger, as seen in Zoids Genesis, possess the unique ability to repair its own Zoid Core (this is because of its ability to Evolt, although the limits to this system are unclear). There are also some instances were Zoids are in possession of multiple Zoid Cores (like the Deadly Kong) or that Zoids have modified Zoid Cores (such as the Ultimate Xs). It is unclear if Organoids possess a Zoid Core; it has been seen in the case of Shadow, however, that a deceased Organoid will turn to stone, just as a Zoid would. Organoid wounds may be healed by Zoid Magnite rock, which is found in active volcanoes. A Core also contains DNA, making possible cloning and genetic engineering.
Many scientists have tried fusing Zoid Cores together, or altering DNA (usually illegally) to create new Zoids; often these plans end in failure. Some successful examples are seen in Zoids: Chaotic Century, where Hiltz creates the Death Stinger using his Organoid, Ambient, to fuse the Cores of the two scorpion-type Zoids, and where Prozen used the Core of the Death Saurer to create a clone of it. Prozen also created the Geno Saurer by altering DNA from the Death Saurer.
In the New Century manga, Stoller was shown to have been piloting an Elephander with a modified Zoid Core. The result of this was that the Zoid had a 300% power increase, but was unable to sustain it for long period of time.
Although Zoid Cores are the power source for Zoids, it is implied they themselves draw power from external sources. It is said that if the Zoid Eve is destroyed, all Zoids will die. This is subverted in Genesis, where Zoids do not derive their power from Zoid Eve, but rely on a limited fuel called Reggel. Even in Genesis, despite the different power source, if the Zoid Core is destroyed, then the Zoid will die.