Moving the object or moving the camera?

Here are a few examples of ‘moving images’. In the earlier days, the camera was static and the action happened in the fixed frame – just like on a theatre stage.
We were looking at ‘The train approaching’ from the Lumiere Brothers, 1896

Here are more movies from the ‘Lumiere-Collection’. 
The French illusionist George Méliès was a pioneer who brought magic to the movies, active between 1896-1913.

Film was the ideal medium to support his magic tricks as obviuous in Un homme de têtes (or The Four Troublesome Heads) by Georges Melies, 1898 or fully hand coloured in Le Papillon Fantastique, 1909. 
His most famous work is most likely ‘A trip to the Moon’ from 1902, handcoloured.

Different to the static camera in these examples, Dziega Vertov was a pioneer in exploring different techniques. Read film-critique Rogert Ebert’s essay (he was one of the most important film critiques).
Dziega Vertov, A man with a movie camera, 1929

Now, a big jump in movie-history. As the conditions developed and allowed to shoot technically perfect movies, the Dogme movement came in 1995 proposing a manifesto which tried to ‘purify’ filmmaking with concepts that only handheld camera is allowed, all shooting must be done on location with no separately recorded audio, 35mm in colour, no filters and other restrictions.
Although strictly speaking not a Dogme movie, but Blair Witch Project was one of the movies which applied the ideals to make the film more credible, especially with its handheld camera and the movie quality, reminding of an amateur film. The viral marketing campaign also added to the credibility. There was a 2016 remake and also a VR version announced.
Ignoring this specific case, most of the camera movement is up/down (tilt), left/right (shift) or a tracking shot (following the subject). To make it less exhausting and sickness provoking, these movements are usually executed with a proper tripod with a video head (fluid head), allowing smooth shifts and tilts, or for the tracking shots with a dolly or crane. For smaller cameras such as the DSLR, a Gimbal is also a good option with a motorised stabiliser.  or using a so called SteadiCam.
This can be observed in the  currently popular seamless or continuity editing in movies such as Birdman:

Pay particular attention to the movement of the camera in the following examples:
Alain Resnais: Toute la memoire du monde
Eduardo Sánchez, Daniel Myrick: Blairwitch Project 

Martin Scorsese: Hugo 
Orson Wells: Touch of evil
Quentin Tarantino: Kill Bill
Martin Scorsese: Goodfellas
Stanley Kubrick: The Shining

Another way in moving in space or time are Jump Cuts. One of the most classical examples is Jean-Luc Godard’s Breathless. More about it when we look closer at  editing…

Slides  as PDF