The argument from fetal pain is an argument that comes up often. Several states, such as Nebraska, North Dakota, and Texas, have passed similar bills. In fact, as of 2019, 24 states have passed fetal pain bills, limiting abortions after 20 weeks, a reasonable cut-off point at when a fetus can likely feel pain, although pro-life advocates argued it could happen as early as 12 weeks. 
To be clear, the argument from fetal pain is not a good argument against abortion. The pro-life position is that abortion is wrong because it intentionally kills an innocent human person — whether or not that person can feel pain or you do it painlessly. This is where the discussion needs to focus. However, if it can be discovered that the fetus can feel pain at a certain point, we can show that to perform abortions on such an individual would be exceptionally cruel.
Research recently published by Stuart Derbyshire and John Bockmann have made such a discovery.  I first encountered word of this research from an article on DailyMail called “Unborn babies MAY feel pain before the 24-week abortion limit, scientists say” (you can just sense the bias dripping from this headline). Derbyshire and Bockmann do not agree on abortion, but they both agree that we should be honest about what science teaches regarding fetal development and what that should say about abortion practices.
I’m not going to summarize all the findings of the study. It’s only four pages so it shouldn’t take you long to read it. A few takeaways, though:
It has been the case that pain has been tied in to development of the cortex, and when the periphery is connected to the cortex through the spinal cord and thalamus. This doesn’t occur before 24 weeks’ gestation. However, recent findings have called this belief into question, such as a study from 2016 “demonstrat[ing] continued pain experience in a patient with extensive damage to cortical regions generally believed to be necessary for pain experience.” They state that while recent findings have called into question the necessity of the cortex for pain experience, there is now good evidence that all the structures necessary for feeling pain are functional at around 12 weeks’ gestation.
The science has not determined fetuses definitely feel pain at around 12 weeks, but the evidence for it is now quite strong, especially strong enough to re-think performing abortions without giving the fetus pain killers (and they also state that abortions are the only procedures done on fetuses in which the fetuses are not given anything for the pain, as far as they know).
The two authors disagree on whether or not abortions should be done. But what they do agree on is that in second and third trimesters, especially after 18 weeks (where the evidence is stronger, even though there is evidence pain experiences occur at around 12 weeks), the fetus ought to be given anesthesia and analgesia before the abortion.
This last point underscores my earlier point about not focusing on fetal pain as an argument against abortion. Even if the science proved beyond the shadow of a doubt that fetuses feel pain, all the pro-choice advocate need do is argue we should prescribe anesthesia to the fetus in order to kill it. We can at least hold out hope that the fact that fetuses can feel pain and should be given anesthesia before an abortion will help women think twice about killing her child, especially since pain and suffering are important to a lot of people. Also, pro-life people have been sounding the alarm about fetal pain for years now, with the pro-choice left calling them “anti-science” for doing so. This recent research will help validate those pro-life arguments about fetal pain. Rosen, David, “The Likely End to Roe v. Wade“? Counterpunch, 2019, https://www.counterpunch.org/2019/09/13/the-likely-end-to-roe-v-wade/