The TARDIS lands on a spaceship from 28th Century Earth which is trapped in orbit over a planet called the Sense-sphere. The Sensorites below control the minds of the abject crew, feed and care for them, but clearly do not want to kill them. The Sensorites board the ship and steal the high-tech lock from the TARDIS door, which prevents the time-travellers from entering and escaping with the space-ship crew. One of them, named John (Stephen Dartnell) has had his mind nearly destroyed. The Doctor discovers that John was the expedition's mineralogist and had found the planet rich in molybdenum.
Susan has budding telepathic powers and can communicate with the Sensorites. They are a peaceful people--Ian's physical threats and The Doctor's righteous anger frighten them--but though they do not wish to harm the humans they are determined to keep them forever in a pleasant prison and will not think of letting them leave. The Doctor and his companions agree to come down to the planet and talk with their leader.
The Sensorites, it seems, had been visited by travellers from Earth before, whose lust for the planet's mineral wealth left them in a miserable and wretched state. They are, in fact, dying. There are factions who plot to kill the humans, but others hope they will help to cure them of the terrible disease, which Ian contracts by drinking the local water. Eventually, of course, The Doctor solves the mystery, after some harrowing events, and all is well.
The story was well-received despite being delayed by sportscasts. The alien sets were interesting because the set-designer (Raymond Cusick) had been inspired by Antoni Gaudi's design of the Sagunda Familia Church in Barcelona, which has no right-angles. The Sensorites themselves were well-designed-- humanoid but strange, frightening at first, but later, as we learn their history, appearing wise and philosophical. I believe they may have inspired the Ood, who show up much later in the Doctor Who canon.