Following its introduction into Georgia in 2007, African swine fever virus (ASFV) has become widespread on the European continent and in Asia. In many cases, the exact route of introduction into domestic pig herds cannot be determined, but most introductions are attributed to indirect virus transmission. In this review, we describe knowledge gained about different matrices that may allow introduction of the virus into pig herds. These matrices include uncooked pig meat, processed pig-derived products, feed, matrices contaminated with the virus and blood-feeding invertebrates. Knowledge gaps still exist, and both field studies and laboratory research are needed to enhance understanding of the risks for ASFV introductions, especially via virus-contaminated materials, including bedding and feed, and via blood-feeding, flying insects. Knowledge obtained from such studies can be applied to epidemiological risk assessments for the different transmission routes. Such assessments can be utilized to help predict the most effective biosecurity and control strategies.