As we all know that sampling with unequal probability plays most important role in large scale sample surveys, therefore in this monograph some recent developments regarding this topic has been discussed. Moreover since joint probability is difficult calculate therefore some approximations of the joint probability have been derived. Special attention has been given to general theory of arbitrary probability. For this theory sampling with replacement and without replacement are the special cases of this general theory. Generalized Murthy estimator has also been discussed in details.