For many years analysts have investigated some important properties of differential operators. That is, operators that involve derivatives, and multiplication by smooth functions. Their studies lead them to study generalizations called pseudodifferential operators, that have many important applications in mathematics. We will describe some of the study of these operators on weighted Lebesgue spaces and state some recent results concerning a further generalization called "Pseudo-pseudodifferential Operators". In the process we discover that some very old ideas that follow from Hardy's obsession with cricket still hold mathematical relevance today.