During and after the Shabbat Torah reading is the time for misheberachs. These are blessings for those who have been called to the Torah (and their wives, children extended families etc) and also for anyone else who might need a blessing — the community, the sick, IDF soldiers, bar- and batmitzvah children, to name just a few.
The custom of giving misheberachs began in eighth-ninth century Babylon. By the Middle Ages, it had become an entrenched custom around the world. Some rabbis opposed it because they thought it wasn’t fitting to focus on Shabbat on what we lack. Rabbi Yosef Karo, however, saw no problem, with the proviso that you do not make a misheberach for an ill person who may feel sad if you do so.
The misheberach, unlike most other blessings, does not contain God’s name. This gives us greater flexibility in inventing new ones. Rabbi Jacob Emden (18th century) was one of those who opposed the proliferation of misheberachs as they can shlep out the service until noon.