In the paper, the authors review and survey some new results on the large Schr�der numbers. These results were obtained by the authors and their coauthors from January 2016 and can be summarized up as follows. (a) By studying the generating function of the large Schr�der numbers, the authors and their coauthors establish several explicit formulas and a recursive formula for the large Schr�der numbers and present relations between the Schr�der numbers and central Delannoy numbers. (b) By utilizing the Cauchy integral formula in the theory of complex functions, the authors and their coauthors build several integral representations for the large Schr�der numbers and their generating function. (c) By employing integral representations for the large Schr�der numbers, the authors and their coauthors find some properties, including the convexity, complete monotonicity, product inequalities, and determinantal inequalities, of the large Schr�der numbers.