The complexity of a modern receiver and the possible range of circuitry and methods employed are more generally covered in electronics and communications engineering.
The receiver must contain a detector to recover the information initially impressed on the radio carrier signal, a process called modulation.
[1] Gain is required because the signal intercepted by an antenna will have a very low power level, on the order of picowatts or femtowatts.
A very good receiver design may have a noise figure of only a few times the theoretical minimum for the operating temperature and desired signal bandwidth.
Frequency stability; the receiver must stay "tuned" to the incoming radio signal and must not "drift" with time or temperature.
Additionally, the great magnitude of gain generated must be carefully controlled so that spurious emissions are not produced within the receiver.
The detector stage recovers the information from the radio-frequency signal, and produces the sound, video, or data that was impressed on the carrier wave initially.
Once these technical objectives have been achieved, the remaining design process is still complicated by considerations of economics, patent rights, and even fashion.
In order to achieve even a minimal sensitivity, a crystal radio is limited to low frequencies using a large antenna (usually a long wire).
This was developed after the invention of the triode vacuum tube, greatly improving the reception of radio signals using electronic amplification which had not previously been available.
The regenerative receiver also had its heyday at the time where adding an active element (vacuum tube) was considered costly.
Self-oscillation reduced the quality of its reception of an AM (voice) radio signal but made it useful as a CW (Morse code) receiver.
The RF signal from the antenna may have one stage of amplification to improve the receiver's noise figure, although at lower frequencies this is typically omitted.
[2] While the concept of SDR is not new, the rapidly evolving capabilities of digital electronics render practical many processes which used to be only theoretically possible.