Celestial Mechanics in the XXIst century – challenges

This special issue of the European Journal of Physics: Special Topics entitled Celestial Mechanics in the XXIst Century published a set of 15 papers aiming to put in perspective the main problems that are being addressed by the researchers in this area. Our goal is to draw attention to the challenges that they represent so that new approaches may be conceived to foster better and more effective solutions of them. In particular, it is shown points related to a new type of creep tide theory, studies related to the risk of collision of space vehicles with space debris, motion near NEAs, strategies to avoid a collision of an asteroid with the Earth and decay of small satellites in the atmosphere of the Earth are included, since they are hot topics of current research.