Recognition and binding of specific sites on DNA by proteins is central for many cellular functions such as transcription, replication, and recombination. In the search for its target site, the DNA-associated protein is facing both thermodynamic and kinetic difficulties. The thermodynamic challenge lies in recognizing and tightly binding a cognate (specific) site among the billions of other (non-specific) sequences on the DNA. The kinetic difficulty lies in finding a cognate site in mere seconds amidst the crowded cellular environment that is filled with other DNA sequences and proteins. Herein, we discuss the history of the DNA search problem, the theoretical background and the various experimental methods used to study the kinetics of proteins searching for target sites on DNA.