We review currently known results concerning the estimation of an 'imm
une' or 'cured' proportion, and testing for the presence of immunes, i
n censored survival data, suggesting that a firm theoretical foundatio
n now exists for analysis. Two types of estimators, parametric and non
-parametric, are discussed and compared with respect to their theoreti
cal properties, and, by simulation, with respect to their small sample
behaviour. Both estimators have advantages and drawbacks, but togethe
r provide powerful tools for the perceptive analysis of survival data
with, or even without, immune individuals.