Plausible premise poorly executed
The Enterprise arrives at the science outpost on Triacus, only to find the adults dead and the children seemingly unconcerned about that fact. The children are taken aboard the Enterprise and it leaves orbit to take them to a star base. Triacus was the home of a legendary group of marauders and one, Gorgan, still survives. He is capable of dominating young minds and he has taken control of the children. Through them, he generates irrational and paralyzing fear in the Enterprise crew, which allows him to take over the ship. After a few futile attempts by Kirk and Spock to take the ship back, the children are shown images of them playing with their parents and then scenes of their parents' tombstones. Their grief breaks Gorgan's hold on them and Kirk regains control of the Enterprise.
This episode is one of several where seemingly powerful creatures easily take control of the Enterprise. The initial concept is not all that implausible, if a creature can control minds, the softest target would be a child. However, the idea breaks down when the children are then capable of controlling the mind of an adult. A creature with this power would not operate using the weak intermediate of a child, but go directly to controlling the mind of an adult. It is a potentially strong plot weakly executed.

Season three was off to a strong start
Incredibly, the second of the 'children' episodes is even darker than the first (Miri). This atmospheric episode is shrouded in a sense of mystery and dread. I would go so far as to call the episode courageous in it's depiction of evil and willingness to give the children complicity in the adults' deaths. Each individual's insecurities and fears are exploited by the Gorgon, and at the height of the episode Kirk has lost control both of his ship and his entire sense of reality.
While some of the effects are quite gimmicky (the knives), others are effective in their simplicity (such as the summoning of the Gorgon). Overall I found this to be an effective, eerie and surreal episode, although some may dislike the fact that there is no simple moral. The cold finality of much of the death (such as being beamed into deep space) may also upset some. The conclusions/ means of dealing with the Gorgon were also admittedly weak.
Tidbits: It would be interesting to know how attourney Melvin Belli ended up in this role.

One of the Best Episodes Ever
Possibly the most intelligent and daring episode (no babes, no explosions) of all three seasons. It is quintessential Star Trek; searing social commentary disguised as `entertainment', which still "goes over the head" of most viewers, even today. Written by Edward Lakso (whose credits include Mission Impossible, Wild Wild West, Rockford Files, Barnaby Jones, Air Wolf), the plot describes the rise and fall of the Nazi Youth movement, where impressionable teens were encouraged to denounce their parents, swear allegiance to a charismatic govt official and propel his rise to power. Apparently Lakso had been observing China... because when this episode aired in 1968, Mao Tse-tung's Cultural Revolution was two years old, unleashing the identical, devastating, social anarchy. It was if an "angel of evil" (named `Chaos' in this episode) had hibernated after WWII, only to re-appear and initiate the same cycle of destruction, in a different country. In true Biblical, Greek, or Star Wars mythological style, Kirk is forced to confront and subdue his own "beast within" before tackling the external enemy, and exposing the `beautiful' angel for what he is; ugly naked Greed, exploiting innocent minds with the complicity of the "silent majority". If this episode makes you uncomfortable, don't blame it on the primitive production values; look inside yourself and think.

Not one of the better episodes
Captain Kirk and the crew beam to a planet and find many adults dead, but all the children are lively and running around and playing like nothing ever happened. Kirk decides to take them onboard the Enterprise, but he might regret it because soon the children will be taking orders from their 'friendly angel' and then they will make some of the Enterprise crew see things such as knives and swords flying at the ship, by pumping their fists.

Plotwise, "And The Children Shall Lead" is one of the worst episodes of Star Trek - The Original Series. It doesn't have much of anything else working for it either, it's not exciting and it's not even all that interesting. I give the episode two stars instead of just one because it had a good ending even if it was a not so good episode. I don't recommend getting "And The Children Shall Lead" unless you're a major Star Trek fanatic and you absolutely have to have all the episodes in your collection because it's far from being one of the best episodes.

This episode gets a D grade and is ranked 77th out of 80
When the U.S.S. Enterprise finds that all the adults in the Starnes expedition to Triacus have killed themselves, they beam to the planet's surface to investigate. The children, however, are alive and well and strangely oblivious to their parents' fates. They are beamed aboard the U.S.S. Enterprise while Kirk searches for an answer to the strange occurrences. The children summon their "friendly angel" Gorgan, who tells them to take the U.S.S. Enterprise to a planet he can control. By garbling Kirk's words and deceiving Spock, the children are able to take control of the starship. Finally, seeing Kirk's anxiety at the loss of his ship, Spock realizes that something is wrong and helps the Captain regain control. Kirk shows the children tricorder tapes of their parents... and their graves, demonstrating to them that Gorgan is not a "friendly angel" but an evil force. The loss of his believers renders Gorgan impotent and he fades into oblivion.