Biologists have long observed that physiological and developmental processes are insensitive, or robust, to many genetic and environmental perturbations. A complete understanding of the evolutionary causes and consequences of this robustness is lacking. Recent progress has been made in uncovering the regulatory mechanisms that underlie environmental robustness in particular. Less is known about robustness to the effects of mutations, and indeed the evolution of mutational robustness remains a controversial topic. The controversy has spread to related topics, in particular the evolutionary relevance of cryptic genetic variation. This review aims to synthesize current understanding of robustness mechanisms and to cut through the controversy by shedding light on what is and is not known about mutational robustness. Some studies have confused mutational robustness with nonadditive interactions between mutations (epistasis). We conclude that a profitable way forward is to focus investigations (and rhetoric) less on mutational robustness and more on epistasis.