The Fibonacci numbers were first described in Indian mathematics as early as 200 BC; however, they are named after the Italian mathematician Leonardo of Pisa, also known as Fibonacci, who introduced the sequence in his 1202 book Liber Abaci. Interesting patterns in the digital roots and endings of the Fibonacci and Lucas sequences can be easily observed. Divisibility of Fibonacci numbers and characteristic prime factors, along with Fibonacci and fibonorial primes, are discussed in detail. Some unusual and amazing applications of Fibonacci numbers, such as in binary strings, multiple reflections, partitioning of integers, and finding the equivalent resistance of a ladder of resistors, are introduced. Fibonacci numbers are related to the golden ratio, which has a unique characteristic in that it differs from its reciprocal by 1. This characteristic leads to several fascinating properties, which are discussed. Properties of the golden ratio, along with its geometrical connections and misconceptions about the golden ratio, are dealt with in this chapter. The application of Benford law in Fibonacci and Lucas numbers is illustrated. The chapter ends with the amazing fallacy of a missing square, which is covered in detail.