Concrete Outdoor Runs (OUTRUNs) are a characteristic part of organic pig housing. They must allow species-specific behaviours such as rooting and elimination, as explicitly required by organic legislation of the European Union (EU). However, OUTRUN design often fails to fulfil behavioural needs, and excreta can cover large parts of the OUTRUN leading to poor pen hygiene and associated ammonia (NH3) emissions. This review integrates legislative, ethological and environmental requirements for OUTRUNs for organic growing-finishing pigs. While EU regulations specify some welfare-related standards for OUTRUNs (e.g. minimal space allowance), national and private standards interpret some aspects differently, e.g. the proportion of roofed and slatted floor area. Furthermore, reducing NH3 emissions is equally a challenge for organic systems, even though EU legislation does not explicitly refer to OUTRUNs. Depending on the actual use of the OUTRUN for elimination, higher space allowance compared to conventional production norms increases the potential for a large NH3-emitting surface. The design of pen features (e.g. roof, floor, enrichment) can encourage pigs to separate functional areas and consequently reduce the elimination area and associated NH3 emissions. While providing the main lying area indoors, resting outdoors should be possible for sub-groups during the day. A roof protects pigs and resources (e.g. bedding) from adverse weather, but the effect on pig welfare and NH3 emissions is site-specific. A floor design that ensures practicable manure removal and drainage is most important to reduce emissions. Providing opportunities for exploring and rooting in the OUTRUN has particular relevance for pigs’ behavioural needs and can improve pen hygiene by reducing the elimination area. Cooling facilities are increasingly important to prevent heat stress and its detrimental effects on welfare and pen hygiene. Finally, practicability for farmers needs to be ensured for all resources provided in OUTRUNs, as good management is crucial. Research gaps emerge regarding the association between soiling and NH3 and the influence of certain pen features (shape, roof, feeder location, pen partitions and wet areas) on pig behaviour and soiling.