[R] Nonparametric generalization of ANOVA

[blue sky]

My interpretation of the relation between 1-way ANOVA and Wilcoxon's
test (wilcox.test() in R) is the following.

1-way ANOVA is to test if two or multiple distributions are the same,
assuming all the distributions are normal and have equal variances.
Wilcoxon's test is to test two distributions are the same without
assuming what their distributions are.

In this sense, I'm wondering what is the generalization of Wilcoxon's
test to more than two distributions. And, more general, what is the
generalization of Wilcoxon's test to multi-way ANOVA with arbitrary
complex model formula? What are the equivalent F statistics and t
statistics in the generalization of Wilcoxon's test?

Note that I'm not interested in looking for a specific nonparametric
test for a particular dataset right now, although this is important in
practice. What I'm interested the general nonparametric statistical
framework that parallels ANOVA. Could somebody give some hints on what
references I should look for? I have google searched this topic, but
don't find a page that exactly answered my question.