How to find which points intersect with a polygon in geopandas?

According to the documentation:

Binary operations can be applied between two GeoSeries, in which case the operation is carried out elementwise. The two series will be aligned by matching indices.

Your examples are not supposed to work. So if you want to test for each point to be in a single polygon you will have to do:

poly = GeoSeries(Polygon([(0,0), (0,2), (2,2), (2,0)]))
g1.intersects(poly.ix[0]) 

Outputs:

    0    True
    1    True
    2    True
    dtype: bool

Or if you want to test for all geometries in a specific GeoSeries:

points.intersects(poly.unary_union)

Geopandas relies on Shapely for the geometrical work. It is sometimes useful (and easier to read) to use it directly. The following code also works as advertised:

from shapely.geometry import *

p1 = Point(.5,.5)
p2 = Point(.5,1)
p3 = Point(1,1)

poly = Polygon([(0,0), (0,2), (2,2), (2,0)])

for p in [p1, p2, p3]:
    print(poly.intersects(p))

You might also have a look at How to deal with rounding errors in Shapely for issues that may arise with points on boundaries.

Since geopandas underwent many performance-enhancing changes recently, answers here are outdated. Geopandas 0.8 introduced many changes that makes handling large datasets a lot faster.

import geopandas
from shapely.geometry import Polygon

p1 = Point(.5,.5)
p2 = Point(.5,1)
p3 = Point(1,1)

points = GeoSeries([p1,p2,p3])

poly = GeoSeries([Polygon([(0,0), (0,2), (2,2), (2,0)])])

geopandas.overlay(points, poly, how='intersection')

One way around this seems to be to either get a particular entry (which doesn't work for my application, but may work for someone else's:

from geopandas.geoseries import *

p1 = Point(.5,.5)
p2 = Point(.5,1)
p3 = Point(1,1)

points = GeoSeries([p1,p2,p3])

poly = GeoSeries([Polygon([(0,0), (0,2), (2,2), (2,0)])])

points.intersects(poly.ix[0])

Another way (more useful for my application) is to intersect with a unary union of the features for the second layer:

points.intersects(poly.unary_union)