What are: Lamrim, Dzogchen, Mahamudra

Could someone provide a brief (good-SE-answer-size) description of the three terms: Lamrim, Dzogchen, and Mahamudra. Specifically, are they different examples of one particular thing, are they progressive or parallel stages, etc. Also, if there was a way to "map" them against other traditions (e.g. "Lamrim is similar to the Visuddhimagga" etc) that would useful. I've read about all three using the usual sources (Wikipedia etc) but it's like wading through mud trying to get a clear picture.