The exact 'chemistry' of the interaction between sperm and egg depends upon the organism involved - in fact a number of interactions are involved. 

Where fertilization is external, the egg is typically surrounded by a layer of extracellular matrix, known as the jelly coat. 

Proteins on the sperm cell membrane bind to molecular components of the jelly coat.  Often these are proteins which an act to attract the sperm. 

These interactions generally involve lectin-like activities, that is proteins that bding to carbohydrate moieties in the jelly coat.

After the sperm adheres to the jelly coat, it must pass through it.  This is mediated by enzymes on the sperm surface. 

As the sperm moves through the jelly coat it is also modified.  Within the jelly coat, and surrounding the egg's plasma membrane is a distinct layer of extracellular matrix, the vitelline membrane or zona pellucida (in mammals).  

The binding of molecules on the sperm surface to molecules within the vitelline membrane/zona pellucida triggers the acrosomal reaction.  

The details of the acrosomal reaction vary beween species, but in the end it acts to breach the vitelline membrane/zona pellucida and bring the sperm and egg membranes in close physical contact.

At this point another molecular interaction system leads to membrane fusion and the delivery of the sperm nucleus into the egg cytoplasm. 

In different organisms, there are specific variations of this process. 

For example, mammalian sperm are activated (capacitated) while moving through the female reproductive tract toward the egg. 

Interactions between sperm and the cumulus cells that surround the egg are also involved in sperm-egg successful fertilization.