Very limited.
It seems the AQMD (air quality management district) has a problem with small gas motors, too much pollution. Everyone can own a lawnmower, but you can't drive one down the street. Same reason you can't use a pocket bike on public property. So, we're stuck with electrics. The limitations there are also pretty strict. The attraction is the one time fee for license and plate, avoiding annual registration and insurance. They call them motorized bicycles. If it's gas you're pretty much limited to commercial products, again pollution controls. If it's electric and has pedals, you are limited to 1000w and 20mph on level ground, even when pedaling. My bike can hit 25mph on a sprint without a motor. If it's electric only you're limited to 2 gross brake horsepower (1493w), and 30mph on level ground. So,... they don't want you in traffic. Even though bicycles have the same rights to the road as cars. You are supposed to keep to the right as far as it's safe. Safe? That's a judgment call. So, if I don't think it's safe to be riding in glass and gravel, I can use the lane. If you want something faster it has to be called a motorcycle and meet all the DOT restrictions, be registered annually and insured. No wonder we're dependent on foreign oil. With the advances in battery technology and electric motors they need to make electric transportation more attractive, not less.