p53 is the most studied human protein because of its role in maintaining genomic stability. Binding to genomic targets is essential for transcription-dependent p53 tumor suppression, but how p53 selects targets remains unclear. Here, the impact of chromatin context on p53 genome-wide binding and targets selection is discussed. It is proposed that p53 genomic binding serves not only to regulate transcription, but to sense epigenomic changes threatening the genomic integrity. The problem of p53 navigating the human genome is discussed with respect to the degenerate p53 binding motif. This discussion relates to the fundamental problem of DNA binding factors navigating large genomes in search for cognate binding sites.