Not asking for a long discussion, and assume knowlege of ODE

Can you say (as quick tips) any equations NDSolve cannot solve, and what of those it may solve in the future? Assume I have a 1st level ODE book. Its probably true that Mathematica can solve anything the book's Numerical methods describe? And say if DSolve can do things NDSolve cannot (aside from range limitations)?

(or for others who are not sure, is there a class of f(x,y,y',...) you tried and it would not solve for you?)

From Help: "NDSolve solves a wide range of ordinary differential equations as well as many partial differential equations." (it shows many options such as stiffness and method choice. but examples show only simple ODE being solved.)