The ongoing depletion of gold and silver-containing ore deposits demands a shift towards the processing of more complex sources. Leaching of gold or silver from these sources, which are named refractory and are typically low-grade, can be complicated due to one or more of the following effects: (1) kinetic or thermodynamic impediments on cyanide diffusion or on the dissolution of minerals, (2) readsorption of leached gold or silver (preg-robbing), and (3) excessive cyanide consumption due to the presence of cyanicidal agents. This article reviews the occurrence of these effects as a function of the elemental composition and compiles strategies to overcome them. The first type of refractory behavior was found to be related to arsenic or antimony sulfides and sulfosalts, manganese oxides, permanganates, iron sulfides, oxides, and hydroxides, tellurides, as well as different sulfur-containing minerals. In general, most kinetic or thermodynamic impediments are addressed by performing intensive grinding and through oxidation processes for sulfides, such as roasting, pressure oxidation, chemical oxidation or biological oxidation. On the other hand, preg-robbing activity was described as common in ores that contain carbonaceous matter, silicates, and sulfides. Strategies to deal with preg-robbing ores often include the destruction or deactivation of the preg-robbing surface, or the addition of another adsorbent to compete with the preg-robber (carbon-in-leach). Finally, cyanicidal agents include sulfides and compounds containing base metals, mainly copper, iron, zinc, and nickel. In the case of sulfides, performing oxidation processes is common, while base metals often require one or more pre-leaching stages in which they can be partially removed from the ore prior to cyanidation. Even though this review intends to serve as a compendium of strategies directed at improving cyanidation processes depending on the nature of the elements present in a feed, a final discussion stressing the importance of developing ore-specific strategies is given.