Many sampling methods (e.g. rejection sampling) approach the sampling of a distribution $p$ as a problem of sampling from a different and somehow easier distribution $q$ and then correcting or accounting for the difference.
What makes some distributions easier or more difficult to sample than others? How does one find an easy distribution to sample from, for a more difficult one?
Computers can only do pseudo random sampling directly from a Uniform Distribution. Sampling from any other distribution requires some numerical transformations, such as Inverse Transform Sampling.
This method, however, only allows to sample from distribution that have a defined Cumulative Distribution Function that can be inverted - and this is the case for most common distributions such as Normal, Exponential, Beta, etc. - these are the "easy" ones.
However, often times we might need to sample from a distribution whose CDF we cannot (or do not want to) compute, and we only have a Probability Density Function. This is indeed pretty standard, as you can often easily create a PDF with a desired shape, but do not have the means to compute its integral.
These cases, where you cannot use inverse transform sampling, are the "hard" ones, where you need to use Rejection or Importance sampling, with the help of a known distribution that you can sample from directly (via ITS).
