Repunits comprising only the digit 1, such as 11 or 111, are closely related to repetends and period lengths of primes. Some beautiful number patterns and curiosities involving repunits, like cubes of certain n-digit numbers ending in Rn, like 884713 = 692472942511111, are covered in this chapter. The divisibility and factorization of repunits, along with repunit primes, are discussed in detail. The curious connection of repunits with Kaprekar numbers is examined, along with some other special repunits like square-free repunits, Harshad repunits, abundant and deficient repunits, repunit semiprime repunits, Smith numbers, etc. which are also highlighted in this chapter. Based on our investigations, some problems are thrown open to readers, such as ‘to find a repunit number that can be represented as the difference of two squares in exactly three different ways?’, ‘to find a repunit Rp that is divisible by a square, where p is an odd prime?’, and ‘to find an abundant repunit Rn such that n is not a multiple of 6?’.