AbstractGillnets and traps often are considered to have fewer holistic environmental impacts than active fishing gears. However, in addition to the targeted catches, gillnets and traps still cause unwanted mortalities due to (i) discarding, (ii) ghost fishing of derelict gear, (iii) depredation, (iv) escaping or dropping out of gear, (v) habitat damage, and potentially (vi) avoiding gear and predation and (vii) infection of injuries sustained from most of the above. Population‐level concerns associated with such ‘unaccounted fishing mortalities’ from gillnets and traps have been sufficient to warrant numerous attempts at mitigation. In this article, we reviewed relevant research efforts, locating 130 studies in the primary literature that concomitantly quantified mortalities and their resolution through technical modifications, with the division of effort indicating ongoing concerns. Most studies (85) have focused on discard mortality, followed by ghost‐fishing (24), depredation (10) and escape (8) mortalities. The remaining components have been poorly studied (3). All problematic mortality components are affected by key biological (e.g. species), technical (e.g. fishing mechanisms) and/or environmental (e.g. temperature) factors. We propose that these key factors should be considered as part of a strategy to reduce impacts of these gears by first assessing modifications within and then beyond conventional configurations, followed by changes to operational and handling practices. Justification for this three‐tiered approach is based not only on the potential for cumulative reduction benefits, but also on the likely ease of adoption, legislation and compliance.