Classic Doctor Who episodes were recorded on video tape, and all tapes were held by BBC TV. In the 1960s and 1970s, BBC Enterprises made film prints of the episodes for overseas sales (because video tape standards around the world were different, but anyone could use film).

In the early 1970s, BBC TV erased hundreds of video tapes. They either thought that other copies of the shows they were erasing existed elsewhere, or they didn't think the shows were worth keeping. (Remember, this is years before the VCR.)

Over at BBC Enterprises, due to the complex nature of the rights involved, they only had a limited amount of time to sell the films. Any film print which was no longer viable was incinerated. They, also, probably thought the master copies existed elsewhere.

The result is that many television programs from the BBC's earliest years are gone, quite possibly forever.

Over 130 episodes of Doctor Who were lost this way, all from its first seven seasons (1963-1970). However, in the 1980s, some of these episodes were kindly returned to the BBC from overseas television stations which had bought film copies from BBC Enterprises years before. Other episodes have been discovered in private film libraries, held by people who did not know the films were significant.

(I got most of the above information from an article in issue #253 of Doctor Who Magazine.)

Overseas television stations sometimes censored the episodes, so the returned product was sometimes missing footage. Conversely, censored clips have sometimes been returned for episodes which are still missing. In other cases, clips which had been sent to BBC news programs as excerpts still exist.

Photos of the episodes, taken by a person photographing the television set while the episodes aired, exist. Also, some fans recorded each episode's audio by placing a tape recorder next to their television speakers. These photos and audio recordings were later welcomed at the BBC with open arms, as they were desperate to have any kind of recording at all for the programs they had lost. The audio recordings have been cleaned up and commercially released, so every missing Doctor Who story is at least available on audio.

Old audio tracks and recovered film prints in poor condition are enhanced and taken care of by a group of people who have become known, unofficially, as the Doctor Who Restoration Team. These guys are headed by Steve Roberts, and they do an outstanding job.

There are 95 episodes of Doctor Who still missing.

Early Doctor Who episodes had individual titles. Starting in May 1966, each episode was simply known as a part of an overall story title.

Each missing episode is in black and white and is about 22.5 minutes long, with no place to break for commercials. The beginning of each episode shows the episode title and author. Cast and crew credits appear at the end.

Wikipedia has a more detailed article containing some interesting history.

But by far, the definitive work which explains the reason for the episodes' destruction, describes the way some episodes have been found and cleaned up, and exhaustively provides far more information about the entire subject than you could possibly imagine exists, is the book Wiped! Doctor Who's Missing Episodes by Richard Molesworth. This book is the one-stop shopping center for everything there is to know about the entire subject. It breaks down a gigantic amount of information into easily understood sections, is very well written, and covers every single minute detail and aspect of the entire situation.

The following is a list of all missing episodes, in chronological order of broadcast. If you find any, please contact the British Broadcasting Corporation.