Structural studies have shown that four G-tracts along a DNA strand are the minimal requirement for intramolecular G-quadruplex formation. Longer DNA sequences containing multiples of four G-tracts could, in principle, form higher-order structures based on multiple G-quadruplex blocks. This latter condition is abundantly verified for the telomeric single-stranded overhang (~200 nt) consisting of tens of TTAGGG repeats, thus opening new interesting questions about the structure of the "real" telomeric DNA. How many quadruplex units form in the human telomeric overhang? Which type of quadruplex topologies? Do they interact or not? What about their binding properties? Although many of these questions are still unanswered, recent experimental and computational studies have begun to address them. The existence and relevance of these higher-order quadruplex structures in the human genome is now an interesting and stimulating research topic in the quadruplex field. The recent results, the unsolved problems, and the future prospects for understanding higher-order telomeric quadruplex structures are the main topics of this review. Other studies on long telomeric RNA sequences and on other intramolecular (non telomeric) DNA higher order quadruplex structures are also presented.