REDUCING CONCUSSIONS BY TACKLING THE WAY RUGBY PLAYERS DO. This article on the Quartz website by Aamna Mohdin points out that the rate of concussions in professional football is much greater than in rugby (which has not had a one billion dollar settlement with injured players). Notably rugby players do not wear helmets. Mohdin has descriptions and videos of the rugby tackle. The rugby player tackles with his shoulder. In contrast, football players use the heads up tackle. Despite the risks of head injuries, the heads up tackle is still being taught. Mohdin has a link to an instructional video teaching how to use the heads up tackle.
The Seattle Seahawks have been teaching their players to use rugby tackles for the last four years. Their coach is Pete Carroll, who has had great success at both the college and the professional level.
When I was a boy, it was the shoulder tackle that was taught. I suspect that the apparently improved helmets encouraged the abandonment of the shoulder tackle.