A Chi-square test or ?2 test is an statistical hypothesis test in which sampling distribution of the test statistics is defined as a chi square distribution while either the null hypothesis is true or it is asymptotically true. Generally in this situation the sampling distribution may be used to approximate the Chi-square distribution. A few examples of chi-squared tests (if the chi-square distribution is approximately valid) are:
Pearson’s chi-square test or chi-square goodness of fit test or also known as chi-square test for independence.
Yates’ Chi-square test or Yates’ correction for continuity
Linear-by-linear association chi-square test
Mantel-Haenszel chi-square test
Portmanteau test in time-series analysis (a test for the presence of autocorrelation)
Likelihood-ratio test: it is used in general statistical modeling
Besides this, chi-square distribution helps to test the variance of a normally distributed population which has a sample variance based value. Although it is not a common practice is study due to its complication.