  The investigation of the ideal class group $Cl_K$ of an algebraic number
field $K$ is one of the key subjects of inquiry in algebraic number theory
since it encodes a lot of arithmetic information about K. There is a
considerable amount of research on many topics linked to quadratic field class
groups notably intriguing aspect is the divisibility of the class numbers. This
article discusses a few recent results on the divisibility of class numbers and
the Izuka conjecture. We also discuss the quantitative aspect of the Izuka
conjecture.
