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On the delete menu with vertices selected, I am presented with two options(among others), dissolve, and limited dissolve. What is the function of each, and when should I use each?

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As per the wiki

A dissolve

...effectively turns the selection into a single N-gon. Dissolve works slightly different based on if you have edges, faces or vertices selected. You can add detail where you need it, or quickly remove it where you don't.

While a limited dissolve

...reduces detail on planer faces and linear edges with an adjustable angle threshold.

From experience, you would use a dissolve to create one large N-gon from several vertices while a limited dissolve can be used to remove excess geometry.

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    $\begingroup$ Note, in 2.67 vertex dissolve has an option Face Split which avoids creating ngons from all surrounding faces and isolates the dissolve. So if a vertex has 3 connected edges, the resulting face will only have 3 sides. $\endgroup$
    – ideasman42
    Jun 1, 2013 at 1:58

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