"Spermatogenesis is the process by which male spermatogonia develop into mature spermatozoa, also known as a sperm cell."

The cycle of the spermatogenesis takes 64 days and can be broken down into two successive sections:

Spermatocytogenesis: primitive cells called spermatogonia increase in number by mitosis.

Spermiogenesis: spermatids change in form during spermiogenesis.  They change into the streamline spermatozoa adapted for fertilization.

Oogenesis is the process by which the ovum is developed. "Oogenesis consists of several sub-processes: oocytogenesis, ootidogenesis and finally maturation to form an ovum. Folliculogenesis is a separate sub-process that accompanies and supports all three oogenetic sub-processes." 

Oocytogenesis: starts with the process of developing oogonia. This stage is complete either before or shortly after birth.

Ootidogenesis: when the primary oocyte develops into an ootid. This is achieved through the process of meiosis.  The ootid eventually matures into an ovum.