Applications of the luminescent materials cannot be overemphasized. Notwithstanding the numerous phosphors available for various applications, researchers are always interested in discovering new ones with high efficiencies and exotic properties. Among various hurdles that hamper these efforts, the concentration quenching of luminescence is most frequently encountered. Several investigations have been directed toward overcoming this issue. These studies have led to some insight into dodging this problem. The systematic efforts to get around the problem of concentration quenching are reviewed here. Important systems in which no concentration quenching has been observed are discussed. The review provides a clue to search for the new systems which could exhibit lack of concentration quenching.