General Notes
When used to compare a set of data against a reference distribution, this is referred to as the one sample "K-S" test or the K-S Goodness of Fit test.
There is also a two-sample K-S test that is used to compare the empirical distribution functions of two samples.
From NIST - Kolmogorov-Smirnov:
The Kolmogorov-Smirnov (K-S) test was originally proposed in the 1930's in papers by Kolmogorov (1933) and Smirnov (1936). Unlike the Chi-Square test, which can be used for testing against both continuous and discrete distributions, the K-S test is only appropriate for testing data against a continuous distribution, such as the normal or Weibull distribution. It is one of a number of tests that are based on the empirical cumulative distribution function (ECDF).
Per Fundamental Concepts in the Design of Experiments (Hicks), the one sample Kolmogorov-Smirnov test for goodness-of-fit might be preferred over the Shapiro-Wilk test when the sample size exceeds 50.
Assumptions
Per NIST: "The K-S test is only appropriate for testing data against a continuous distribution."
References
NIST - Kolmogorov-Smirnov test description
NIST - Kolmogorov-Smirnov test detail
Wikipedia - Kolmogorov-Smirnov