Possible collisions of asteroid Apophis with the Earth in the 21st century are considered. In spite of the refinement of its orbit in 2012-2013, a number of collisions are still possible, so that Apophis should continue to be considered as a hazardous asteroid. Usually after the refinement of an asteroid’s orbit, the object can be removed from the list of hazardous objects; examples are asteroids 2011 AG5, 2007 VK184 and many others. Apophis is an exception to this trend. A list of more than 100 possible collisions of asteroid Apophis with the Earth is presented, including relative positions and ranges of initial conditions that lead to collisions or to gaps between the asteroid’s orbit and the Earth. The stability of these characteristics under small changes in the motion model and in Apophis’ initial conditions is discussed. The results concerning asteroid Apophis derived by NASA are considered as well; these are in good general agreement with our results. However, NASA presents only 9 probable collisions in the 21st century, with large gaps. Complicated structure of the gaps, similar to a fractal structure, is discussed. The cause of this is the resonant returns of the asteroid under discussion. This similarity to fractal structure must be taken into account when considering the elimination of possible collisions. Pecularities of the motion of Apophis, connected with resonant returns, are similar as for other hazardous objects. Investigation of these pecularities is a very important problem. Refs 21. Tables 3