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Could somebody explain to me (non-physicist) what the principles at play are?

Is it "simply" that they fire a strong laser at the front of the object to slow it down, so that orbital mechanics do the rest and make it burn up?

Do lasers really allow you to "push" things?

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not a physicist, but an electrical engineer.

At least 2 principles that I know allow a laser to push things:

1) photons do have impulse, given by its energy divides by the speed of light. This causes Radiation pressure (see https://en.wikipedia.org/wiki/Radiation_pressure ) 2) if a laser vaporises part of a structure, the resultant gas will push against the structure, delivering momentum

Both principles have an impact, and in this case, I think the second one is the one that causes most of the impulse.

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