  Since the famous paper written by Kaplan and Meier in 1958, survival analysis
has become one of the most important fields in statistics. Nowadays it is one
of the most important statistical tools in analyzing epidemiological and
clinical data including COVID-19 pandemic. This article reviews some of the
most celebrated and important results and methods, including consistency,
asymptotic normality, bias and variance estimation, in survival analysis and
the treatment is parallel to the monograph Statistical Models Based on Counting
Processes. Other models and results such as semi-Markov models and the
Turnbull's estimator that jump out of the classical counting process martingale
framework are also discussed.
