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Theoretical framework on which quantum field theories are based, theories based on framework include:
so basically the entire Standard Model
The basic idea is that there is a field for each particle particle type.
And then those fields interact with some Lagrangian.
One way to look at QFT is to split it into two parts:
Then interwined with those two is the part "OK, how to solve the equations, if they are solvable at all", which is an open problem: Yang-Mills existence and mass gap.
There appear to be two main equivalent formulations of quantum field theory:
Video 1. Quantum Field Theory visualized by ScienceClic English (2020) Source. Gives one piece of possibly OK intuition: quantum theories kind of model all possible evolutions of the system at the same time, but with different probabilities. QFT is no different in that aspect.
Video 2. Quantum Fields: The Real Building Blocks of the Universe by David Tong (2017) Source. Boring, does not give anything except the usual blabla everyone knows from Googling:
Video 3. Quantum Field Theory: What is a particle? by Physics Explained (2021) Source. Gives some high level analogies between high level principles of non-relativistic quantum mechanics and special relativity in to suggest that there is a minimum quanta of a relativistic quantum field.