Word processor support in citation managers: Is there a better way?

Citations of the relevant literature are an essential feature of scientific papers. Reference Manager software helps adding these citations and creating a bibliography. Are there differences in how reference managers work together with your word processor of choice?

This is a companion discussion topic for the original entry at https://blog.front-matter.io/mfenner/word-processor-support-in-citation-managers-is-there-a-better-way