How do mains voltage LED filament bulbs work?
What are the filaments inside a bulbs


See Wiki - LED filament for the idea behind these lightbulbs. Quotation: -


  The LED filament is composed of a series of LEDs on a transparent
  substrate, referred to as Chip-On-Glass (COG). These transparent
  substrates are made of glass or sapphire materials. This transparency
  allows the emitted light to disperse evenly and uniformly without any
  interference. An even coating of phosphor in a silicone resin binder
  material converts the blue light generated by the LEDs into a mixture
  of red, blue, and green light to create a specified light temperature.
  Degradation of silicone binder, and leakage of blue light are design
  issues in LED filament lights. Positive benefits of the LED design are
  potential higher efficiencies by the use of more LED emitters from
  lower driving currents – major benefit of the design is the ease with
  which near full 'global' illumination can be obtained from arrays of
  filaments.




Picture taken from here

It's difficult to say how many LEDs are involved but if they are 3 volt LEDs and the mains is rectified and smoothed from 230 VAC to 324 V DC then 100 or so of these substrated LEDs might be used and also a current limiting resistor or transistor circuit.


  What is the circuit?


It could be as simple as a bridge rectifier, smoothing capacitor and a linear current regulator with all the LEDs in series.


  Are there capacitors or resistors involved?


Almost certainly.