What important ideas came since Nelder and McCullagh's book Generalized Linear Models (a 40 year old book)? I read not too long ago Nelder and McCullagh's book Generalized Linear Models and thought the book was fantastic and I consider it a useful manual on the subject. Not surprising that's the case, considering Nelder's one of the authors.
However, the book is 40 years old, and surely things have changed since when the book came out. Simon Wood's book, Generalized Additive Models, is very good, but the book focuses on GAMs, not GLMs. (Yes, GAMs generalize GLMs, but I do think focusing on GLMs specifically is worthwhile.)
Hence, what would be the most important developments since Nelder and McCullagh's book came out regarding GLM theory and application? What am I missing from just reading that book? How should I supplement my knowledge?

To add to Ben's great answer, since Nelder and McCullagh's GLMs (1983) is mentioned, I think it's fair to say that one important development after that was the extension of the GLM idea to other families of distributions, that generalize the single parameter exponential family.
Important examples include both Beta and Dirichlet regressions, which are not GLMs in the N&M sense (see Why Beta/Dirichlet Regression are not considered Generalized Linear Models?). Both are important to analyze continuous compositional data, in univariate and multivariate senses, respectively, as alternatives to log-ratio analysis. Here are the respective references:

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*Ferrari, Silvia, and Francisco Cribari-Neto. "Beta regression for modelling rates and proportions." Journal of applied statistics 31, no. 7 (2004): 799-815.

*Hijazi, Rafiq Hamed. Analysis of compositional data using Dirichlet covariate models (thesis). American University, 2003.
The Bayesian treatment of conditional models is much more direct, but only more recently the machinery (i.e. software and hardware) made it accessible to be used by most (BUGS was release in the 90s, for example). I cannot pinpoint a single reference for this however, but reading on Bayesian GLMs can be of help.
