In the serial, the time travellers the First Doctor (William Hartnell), Ian Chesterton (William Russell), and Barbara Wright (Jacqueline Hill) befriend Vicki (Maureen O'Brien), an orphan girl marooned on the planet Dido who is being threatened by an apparent native of Dido called Koquillion (Ray Barrett) while awaiting rescue.

The Rescue was written as a short vehicle to introduce Vicki as the new companion, replacing the Doctor's granddaughter, Susan.

The trio soon encounter two survivors of a space crash, Vicki (Maureen O'Brien) and Bennett (Ray Barrett), who are awaiting a rescue ship that is due to arrive in three days time.

Koquillion encounters the time travellers and attacks, pushing Barbara over a cliff and temporarily trapping Ian and the Doctor.

However, when Ian and the Doctor reach the ship, tempers are fraught because Barbara mistook the Sand Beast for a threat and killed it.

The Rescue was written as a short vehicle to introduce Vicki as the new companion, replacing the Doctor's granddaughter, Susan.

[5] Producer Verity Lambert had originally booked Pamela Franklin to portray Jenny (originally called Saida) in the previous serial, The Dalek Invasion of Earth, and continue as Susan's replacement; however, Lambert soon changed her mind,[6] and outgoing script editor David Whitaker was commissioned to write a two-part serial to introduce Vicki.

With budgeting tight, Barry decided to reuse the score from his previous serial, The Daleks, composed by Tristram Cary.

[9] When O'Brien met with the show's creator Sydney Newman, he told her that they were considering having her cut her hair and dye it black.

After Barrett fell asleep in the studio, the cast and crew left and switched off the lights to make him believe that he had slept all night.

In the scene where Barbara shoots the sand beast, the powder in the prop detonated prematurely, and Hill was treated for shock and a sore face.

At the BBC's Programme Review Board after the second episode, Sydney Newman said that O'Brien had "made a great impact" on the show, noting that her performance had improved others.

In The Discontinuity Guide (1995), Paul Cornell, Martin Day, and Keith Topping wrote that the serial "just about works" as an introduction to Vicki, "but it's too inconsequential to sustain any real interest".

[25] In The Television Companion (1998), David J. Howe and Stephen James Walker described the story as "one of the best examples of character-driven drama from this period of the series' history", praising the character of Vicki, though noting that some parts of the plot remained unexplained.

[26] In A Critical History of Doctor Who (1999), John Kenneth Muir lauded O'Brien's performance despite Vicki being "a fairly obvious Susan surrogate", and enjoyed the emotional scenes and climax.

[27] In 2008, Patrick Mulkern of Radio Times described the serial as a "neglected gem" with a strong debut for Vicki and many production improvements, though noted that the mystery was "a tad obvious".

[28] In 2009, DVD Talk's Stuart Galbraith IV felt that the story was strong with a "smart, if somewhat predictable climax and resolution" that worked due to the dialogue.

[32] The Rescue was released on VHS as a double-pack with The Romans by BBC Video in September 1994, with the cover designed by Andrew Skilleter.