Star formation is a fundamental field in astrophysics, within which the core mass function (CMF) of molecular clouds is a hot topic. Different models of molecular core evolution predicted different CMFs. Comparing CMF with stellar initial mass function (IMF) would help reveal the origin of stellar mass and the conversion rate between cloud cores and stars. In this review, we describe two expressions of CMFs, namely, differential CMF and cumulative CMF. When the sample size is small, cumulative CMF can clearly reflect the number of cloud cores. When the sample size is big, differential CMF is a straightforward representation based on binning the data. We research and read most of the highly cited papers published before 2013 that are related with CMF. Based on these studies, we found that two function forms of CMF, namely, power law CMF and log-normal CMF, are widely used. Fitting a log-normal function to CMF produces a better result for cores under the influence of turbulence. The CMF power law index fluctuates in a fixed interval and varys from region to region. The stellar IMF is generally thought to follow a power law function. Many research work indicate that CMF resembles IMF. However, some recent researches conclude that CMF tends to be different from IMF. The conclusion is based on that (1) fitting a power-law directly to an arbitrary cumulative function is unreliable, (2) cumulative CMF can be approximated by a power-law only at M ? Mmax (or Mmax -→∞), (3) with fitting CMF Monte Carlo approach gets a flatter index thanβ.