How to blur a face or part of a video
Blur a face in Video by Zaweba by giving a blur effect a mask, then using mask tracking so the blur follows the person through the shot.

Blurring a face in Video by Zaweba means applying a blur effect that only acts inside a mask, then tracking the mask so it follows the face. Draw an ellipse round the face, give the blur that mask, and press Track forward; the mask's position is keyed on every frame and the blur goes wherever the face goes. It's free and done entirely on your PC.
The same steps hide a number plate, a screen with private details, a house number or a logo you don't have permission to show.
Drawing the mask
Select the clip and add a mask. One click makes a rectangle, ellipse or star, and an ellipse is the obvious shape for a face. Drag it into place on the preview and resize it so it covers the whole face with a little room to spare. For awkward shapes, draw a polygon, a pen curve or freehand instead.
Give the mask some feather so the blur fades into the picture at its edge rather than ending in a hard line. Expansion grows or shrinks the mask without redrawing it, which is handy if the face gets bigger as someone walks towards the camera.
Blurring only inside it
Add a blur from the Effects tab. Gaussian blur is the usual choice for a face; it's soft and makes features unreadable when set strongly enough. Then give the mask to that single effect so it only acts inside the mask, rather than the mask cutting the clip itself. The rest of the frame stays sharp and untouched.
Set the blur strongly. A light blur can leave a face recognisable, which defeats the point. If you'd prefer a blocky look, the mosaic effect from the stylise group works the same way.
Making it follow the face
Put the playhead on the first frame where the face appears, with the mask in place, and press Track forward. Video by Zaweba follows the picture inside the mask and keys its position on every frame. Track back works the other way from the playhead, so you can start in the middle of a shot where the face is clearest and track both directions.
If the head turns or the person moves closer, a later tracking mode follows two detailed spots to key rotation and scale as well. For flat things that tilt away, such as a sign or a phone screen, 'Follow in perspective' tracks four spots and pins the mask's corners to them.
Checking every frame
Tracking is good but not infallible. A face passing behind someone, a fast turn or motion blur can make the mask slip. Play through at normal speed, then scrub slowly through the hard moments. Where it drifts, move the mask back by hand at that frame; it's keyed there and the rest stays as tracked. You can also stop the track before a difficult moment and start again after it.
For privacy work, be strict. One frame with the face exposed is enough for someone to pause on it.
Several faces and other cases
Each mask has its own tracking, so add one mask per face and give each to the blur. For a face that stays in one place, such as an interview subject who must stay anonymous, you might skip tracking altogether and keyframe the mask by hand at a few points.
If the sound gives the person away too, bleep or lower the parts where they're named, and consider the pitch shift effect in the sound library for their voice. Then export with Ctrl+E; the blur is rendered into the picture and can't be undone by whoever watches the file.