If your vehicle is showing oil leaking visibly around the oil filter housing, here are the most likely causes and the parts you'll need to fix each one.
The rubber O-ring from the old oil filter stuck to the housing during an oil change, and the new filter was installed directly over it. This prevents a proper seal and causes a rapid, heavy oil leak.
The spin-on oil filter or the plastic cartridge housing cap was not tightened to the proper specification during the last maintenance, allowing oil to seep past the seal under pressure.
The gasket that seals the entire oil filter housing assembly to the engine block has hardened, flattened, or cracked due to age and repeated heat cycles.
Many modern vehicles use plastic oil filter housings that can become brittle over time and crack. This is frequently exacerbated by over-tightening the cap during an oil change.
The oil pressure sensor is frequently mounted directly on or near the oil filter housing. Its internal diaphragm can fail, causing oil to leak through the sensor body or its threads.
If your vehicle has an engine oil cooler sandwiched between the filter and the housing, the seals connecting them can degrade and leak oil down the side of the housing.