Toda no doubt made some big strides when computing unstable homotopy groups $\pi_{n+k}(S^n)$ for $k < 20$ which his collaborators later improved upon.

The methods he used are documented in his book: "Composition methods in homotopy groups of spheres". However I find the book quite archaic and old-fashioned.

Is there a survey of Toda's work using modern language? Especially any modern insights that simplify his computations.

I find that unstable homotopy groups are neglected to some extent in modern work as there is a lot of focus on the stable case. And apart from Toda's work I cannot find any detailed surveys on these computations.