Recent developments in multiplicity surveys have been examined. A comparison of the conventional survey estimator and the multiplicity estimator has been presented. Multiplicity estimators for stratified multistage cluster samples have been discussed. New methods to reduce the amount of multiplicity Information is presented. Among these “completely nested inverse multiplicity estimator”, 'superstage inverse multiplicity estimator”, and the “use of multiple counting rules” are considered. Computational procedures for the samp­ ling variances of various estimators have been mentioned.