California recently passed several laws to make it easier for the market to provide housing.
However, local governments are still the ultimate deciders and many of them are opposed to new housing, such as in the SF Peninsula.
Other parts of CA are less resistant to new housing. In LA's downtown, for example, almost 50,000 units of new housing are being brought online between 2016-2021. In both Korea Town and Hollywood, more than 5,000 new units have come online in the past 3 years (and they're already the densest neighborhoods). In Marina Del Rey and Playa Del Rey, roughly 2500 new units have opened/will open up in 2018 and 2019. Along the Metro Expo Line, more than 25,000 residential units within 4 blocks of a station are planned or already under construction. Inglewood will see somewhere between 500 and 2500 new apartments in the neighborhood around the Sofi Stadium, not including other residential development. Even Santa Monica will see roughly 2000 new apartments over the next 2 years.
Edit: these are just the developments that I'm aware of. There are plenty more. If you're interested in following LA-area development, there are several Facebook groups devoted to this subject.