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Objects that are on the verge of being black holes but actually are distinct in many ways are called quasiblack holes. The main properties are: there are infinite redshift whole regions; the spacetimes exhibit degenerate, almost singular, features but their curvature invariants remain perfectly regular everywhere in the limit under discussion; outer and inner regions become impenetrable and disjoint, although, in contrast to the usual black holes, this separation is of a dynamical nature, rather than purely causal; for external far away observers the spacetime is virtually indistinguishable from that of extremal black holes. If only finite stresses are allowed then quasiblack holes must be extremal. Mass formulas for these objects can be derived and an entropy can be as well assigned to them. Here we also sketch the Carter-Penrose diagrams for quasiblack holes emphasizing the differences to the corresponding black hole diagrams. [1] J. P. S. Lemos, O. B. Zaslavskii, "Quasiblack holes: definition and general properties", Physical Review D 76, 084030 (2007); arXiv:0707.1094 [gr-qc]. [2] J. P. S. Lemos, V. T. Zanchin, 2010, "Quasiblack holes with pressure: Relativistic charged spheres as the frozen stars", Physical Review D 81, 124016 (2010); arXiv:1004.3574 [gr-qc]. [3] J. P. S. Lemos, O. B. Zaslavskii, 2011, "Entropy of extremal black holes from the entropy of quasiblack holes", Physics Letters B 695, 37 (2011); arXiv:1011.2768

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