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I have lots of points representing buildings, scattered on top of polygons representing output areas of a city. I'd like to select only those points that have a certain descriptor in their database, and make a new layer with them.

This is done a number of times with a view to then counting how many buildings of each category are in each output area. I think I'm going to use a spatial join for that.

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    You can select by an attribute on your point layer. Then select the layer in the table of contents, right click choose save as, give a new name and specify to save only selected features – Gerardo Jimenez Jul 28 '16 at 16:47
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You almost described the steps necessary to create the new layer: Open the attribute table for the point layer and choose the option 'Select features using an expression'. In the new window you can enter an expression like "column_name" = 100 (or choose the wanted column from "Fields and Values") and press Select.

After that right-click on the layer and choose "Save As...". Make sure that you select the "Save only selected features" in the save dialog.

For the calculation of the number of buildings inside the output areas have a look at the "Count points in polygon function" from the vector tools.

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If you're going to do this often, you could also consider making a model from the Processing Toolbox which would automatically select features based on an expression you provide and save the selected features in one go:

Model

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