What is inclusive fitness theory, and what is it for?

Inclusive fitness theory is a cornerstone of modern evolutionary biology, yet critics contend it is not general but subject to serious limitations, and is ripe for replacement, for example by multilevel selection theory. These critics also question empirical predictions made using inclusive fitness theory, such as on sex allocation, and the use of statistical concepts in understanding responses to selection. Here I summarise recent resolutions of these criticisms, then discuss what inclusive fitness theory actually is and why it is useful for evolutionary biology. In doing so I focus on recent developments in evaluating causal explanations for social evolution, and the role of inclusive fitness theory in explaining group adaptations, including the major transitions to obligate eusociality and eukaryotic multicellularity.