A good rule of thumb is anything over $500 in labor and materials might require a permit. This is also the CA requirement for hiring a licensed individual to perform the work.
Always best to call your building department and ask, but generally speaking, work that involves opening walls, cutting pipes or wires, combustibles (fireplaces, furnaces, water heaters) air quality (HVAC), modifying the structure (foundation, framing, roofing, windows, waterproofing, stairs, etc.) will definitely require a permit. Smaller jobs like painting a room, refinishing floors, replacing a door, changing a light fixture or faucet using existing hookups - things that fall clearly into the “handyman” realm, probably won’t require a permit. Anything you could call a “remodel” will definitely need permits.