The 1964 story about the Doctor meeting Marco Polo is one that’s completely lost. The BBC, more concerned in those days with economy than with archiving the shows they broadcast, taped something else over it. All that survives are a soundtrack recorded and a few still photos taken by a dedicated fan; these are used to re-create a half-hour long synopsis of the 7 missing episodes as an extra feature on the The Edge of Destruction DVD.

The footprints Susan and Barbara found at the end of the previous episode have nothing to do with this story, except that they’re in a snowy mountain pass in the Himalayas.
The Doctor’s group is briefly menaced by some Mongols who think that the strangers are evil spirits, but they are almost immediately rescued by that well-traveled and famous Venetian gentleman whose name has become a popular children’s swimming game. He invites them to the safety of his caravan. Since the Tardis is still experiencing some malfunctions from the last story, they agree.
Marco Polo is played by Mark Eden who, as I mentioned in my review of An Adventure in Space and Time, was in The Prisoner and had a small role at the beginning of Dr. Zhivago (“We couldn’t admire his poetry when we weren’t allowed to read it!”)

With Marco Polo is a young lady named Ping Cho. He is escorting her from Samarkand to be married to the very old Kublai Khan. Ping Cho becomes friends with Susan, since they’re about the same age.
There’s also a dastardly Chinese nobleman who will be making trouble for Marco Polo and the Tardis Four as they make their way to Peking.
For Marco has decided to present the Tardis to Kublai Khan in hopes that the great emperor will accept this impressive “caravan” as a bribe and allow him to return home to Venice. He’s been away since he first traveled to “Cathay” (the old European name for China) with his father and uncle as a lad of 21 in 1271, and that was more than 20 years ago.
The Doctor seems characteristically clueless and unsympathetic. “That’s your problem, not mine,” he huffily tells the explorer.
“I have just made it yours as well,” Marco Polo retorts, and confiscates the Tardis’s key.
They trundle the Tardis across China in a horse-cart.

A voiceover narration from Marco Polo as he writes in his journal keeps the viewer apprised of their progress, and also gives us an outsider’s perspective on the Doctor and his companions. A map of medieval China with an animated line moving across it shows how the caravan moves from city to city on this long journey.
Along the way, Ping Cho tries to help her new friend Susan by stealing the Tardis key, but the escape attempt is foiled. Ian tries to tell Marco Polo that the Tardis is a time machine, but Marco’s never looked inside it and doesn’t believe him.
When they finally get to Peking, the reluctant bride then tries to escape herself rather than marry a man as old as her grandfather, but she’s brought back to the summer palace. This condensed version of the story doesn’t tell me what happens to her after that.

The Doctor hits it off with the aged Kublai Khan and they play backgammon together. The Doctor wins every game and piles up a lot of loot, until he stakes it all on the Tardis… and then he loses everything.
It looks like they’ll all be living in the 1290s for a while, but suddenly there’s a fight within the city, and Marco Polo lets the Doctor have the Tardis key. The Doctor et al dash into the Tardis, which disappears before the astonished eyes of both Marco Polo and Kublai Khan.
Khan asks Marco if he’ll tell the people back home about the amazing thing he’s just seen, which hints that Khan will let the explorer go home. (As a matter of fact, he does, and Barbara told Marco he would return to Venice one day). Marco Polo responds that he’s seen a lot of incredible things in Cathay, but no one in Venice would believe this.
He wonders where, and when, the group of time-travelers is now, but we don’t get to see it.
The DVD informs me that a full-length radio version of this lost story is also available.