Extract values from feature class to points

I am using ArcMap 10.3.1. I have a polygon feature class along with a point feature class. I want to extract values from one field of my polygon feature class to my points.

To specify, I have a geologic map (so basically a polygon feature class) with a RockType field in its attribute table. I have a bunch of points and I want to know what the RockType of each point is based on the polygon feature class that has the RockType field.

I know of the Extract Values to Points and Extract Values to Table tools, but those both require raster datasets, which I do not have. I’m wondering whether extraction by feature class is possible in ArcMap. If so, what tools/codes do I need to perform this task?