Indian recreational mathematician D. R. Kaprekar made significant contributions by discovering various classes of numbers, such as Kaprekar numbers and the mysterious constant 6174, which possesses the unique property that the difference between its digits in descending and ascending orders results in the constant itself, a phenomenon now known as the Kaprekar process. In addition, Kaprekar introduced self-numbers, Harshad numbers, etc. In this chapter, we will discuss some of these marvellous numbers and present the results of our investigation of them, such as ‘no Kaprekar number is known that can be generated by concatenating two sequentially decreasing numbers’, ‘the only known perfect power that is also a Kaprekar number is 9’, etc. The concept of intra-differences applied to five-digit numbers to speed up computations can be extended to higher-digit numbers as well for speedy identification of cycles and fixed points. The majority of self-gaps noted are 10. However, the record gaps between self-numbers continue to increase with higher values of n. Further explorations of maximal gaps, frequently occurring gaps, and missing gaps between self-numbers can be fascinating.