What are soft theorems in context of scalar fields? What are soft theorems? I tried reading Weinberg’s paper but couldn’t understand it. I am very interested in the case of scalars.
 A: Weinberg's paper is indeed hard to comprehend, I remember when I was making my first attempt, it took a long time to understand it and even to this day, I am not sure that I understand it perfectly. Other resources for reading about soft theorems include Peskin (chapter 6) and Weinbergs vol.1 (chapter 13). The book is pretty similar to the paper though, but still usefull...
Before reading the above chapters, I suggest you have in mind that soft theorems are theorems describing scattering processes in which there exists additional low energetic (or otherwise soft) radiation. The Feynman amplitude corresponding to such processes is related to the Feynman amplitude describing the aforementioned processes without including the additional soft radiation via multiplication with a "soft factor". Furthermore, it can be shown that the infrared structure of those amplitudes is universal in the sense that it does not depend on the specifics of the matter fields (i.e. the same for scalars/fermionic fields etc)
I also advice you take a look at
https://canvas.harvard.edu/files/936391/download?download_frd=1&verifier=x0zyaPHMxOvHCcrRCDqlHUqjT4stQ3tv0Z69Eohc
for the scalar case.
