ST_Crosses — Tests if two geometries have some, but not all, interior points in common
boolean ST_Crosses(
geometry g1, geometry g2)
;
Compares two geometry objects and returns true
if their intersection "spatially crosses"; that is, the geometries have some, but not all interior points in common. The intersection of the interiors of the geometries must be nonempty and must have dimension less than the maximum dimension of the two input geometries, and the intersection of the two geometries must not equal either geometry. Otherwise, it returns false
. The crosses relation is symmetric and irreflexive.
In mathematical terms: ST_Crosses(A, B) ⇔ (dim( Int(A) ⋂ Int(B) ) < max( dim( Int(A) ), dim( Int(B) ) )) ∧ (A ⋂ B ≠ A) ∧ (A ⋂ B ≠ B)
Geometries cross if their DE9IM Intersection Matrix matches:
T*T******
for Point/Line, Point/Area, and Line/Area situations
T*****T**
for Line/Point, Area/Point, and Area/Line situations
0********
for Line/Line situations
the result is false
for Point/Point and Area/Area situations
The OpenGIS Simple Features Specification defines this predicate only for Point/Line, Point/Area, Line/Line, and Line/Area situations. JTS / GEOS extends the definition to apply to Line/Point, Area/Point and Area/Line situations as well. This makes the relation symmetric. 
This function automatically includes a bounding box comparison that makes use of any spatial indexes that are available on the geometries. 
Enhanced: 3.0.0 enabled support for 
This method implements the OGC Simple Features Implementation Specification for SQL 1.1.
s2.1.13.3
This method implements the SQL/MM specification.
SQLMM 3: 5.1.29
The following situations all return true
.
Consider a situation where a user has two tables: a table of roads and a table of highways.
CREATE TABLE roads ( id serial NOT NULL, geom geometry, CONSTRAINT roads_pkey PRIMARY KEY (road_id) );

CREATE TABLE highways ( id serial NOT NULL, the_gem geometry, CONSTRAINT roads_pkey PRIMARY KEY (road_id) );

To determine a list of roads that cross a highway, use a query similiar to:
SELECT roads.id FROM roads, highways WHERE ST_Crosses(roads.geom, highways.geom);