The "Neutrodyne" was one particular way of neutralising such circuits,but there are others.
Three terminal devices such as triode valves (vacuum tubes) have a problem with inter-electrode capacitance causing feedback between the output & input elements of the device.
Without any applied operating voltages,the capacitance between,say,Collector & Base is quite small,but when the device is amplifying,the effective capacitance is multiplied by the voltage gain of the stage.
---Look up "Miller Effect",or "Miller Capacitance".
The possibility of mis-tuning the Base & Collector LC networks causing the fed back signal via"Miller Capacitance" to no longer be 180 degrees out of phase,with the Base signal but instead to be"in phase",makes oscillation likely.
A particular kind of Oscillator uses just such a setup----Look up "Tuned Plate-Tuned Grid (TPTG) Oscillator".
Early TRFs (& Superhets) used triode valves,so they all needed to provide some form of Neutralisation.
(Intentionally feeding back a small amount of the output signal ,specially adjusted to be antiphase to the unintentional feedback signal via Miller Capacitance.)
Tetrode & Pentode tubes reduce the inter-electrode capacitance to such a low value that even allowing for Miller Effect,the resulting value of "Miller Capacitance"is still too low to cause instability.
This allowed the use of Un-Neutralised stages in receiver RF & IF stages.
Transmitters usually still used some form of Neutralisation
Along came Solid State----BJTs are triodes,in effect,so Neutralisation was back!
To add insult to injury,early transisators were prone to oscillation at low frequencies as well,so a combined correction was used to cover both LF,& the MF operating frequencies.
This was dubbed "Unilateralisation".
FETS also can exhibit "Miller Effect".