A well written PhD or MSc thesis is often the best way into a new field, ime. If the committee is good on this aspect they'll insist you've put enough detail in for someone to follow along mostly self contained.
The text changes to fit the audience, and the knowledge becomes more accepted (and or fundamental) further down the line.
Is this field specific? I have read survey articles in math and biology, and was told by some of my profs that they use these articles as an introduction to a new field.
A quick Google search seems to show these exist in CS (along with tutorial papers), physics, and chemistry but I'm having a little difficulty finding statistics survey papers (survey methods come up instead).
Is the problem that there aren't enough of them or they are behind paywalls?
Please suggest others if you find them.
Annual Reviews has a bunch of journals for surveys of various fields. Most of them are paywalled, but there's ways around that.
Review articles, sometimes called surveys.
I've always thought that new PhDs would be excellent authors for those, having digested lots literature for their dissertation.