Paraproducts are one of the essential tools of harmonic analysis, used to decompose a product of two functions. Motivated by a similar question in complex analysis, Pott, Reguera, Sawyer and Wick studied the composition of "paraproduct-type operators", to which classical paraproducts belong. Their goal was to find joint conditions on the symbol functions for the composition to be bounded. They classified many paraproduct-type compositions. One of the operators to remain unclassified was the composition of two classical dyadic paraproducts. In this talk, we will discuss the joint conditions for the boundedness of two paraproducts as well as certain weighted inequalities.