Here’s a recent webinar on terraforming Mars from the NASA MAVEN Mission to Mars youtube channel. The TL;DR is that it will be monumentally difficult, but sooner or later we are likely to try it. In the meantime, we shouldn’t get hung up on the feasibility of the endeavour as we make plans for exploring and colonizing Mars.
Along the way is a great deal of information on the history of Mars, including the questionable relevancy of its lack of magnetic field, and details on what it would take to terraform a planet.