Fusarium wilt of banana (also known as Panama disease) has been a problem in Australia since 1874. Race 1 of the pathogen (Fusarium oxysporum f. sp. cubense) is responsible for damage to ‘Lady Finger’ (AAB, Pome subgroup) and other less widely grown cultivars such as ‘Ducasse’ (Pisang Awak, ABB). Subtropical Race 4 (STR4) also affects these cultivars as well as Cavendish cultivars (AAA) in southern Queensland and northern New South Wales where cold temperature predisposition is involved. Tropical Race 4 (TR4) has led to the demise of the Cavendish industry in the Northern Territory, and its presence was confirmed in a North Queensland plantation in 2015, which warranted destruction of all banana plants on the property; as of this writing (April 2019), TR4 has spread to two adjacent properties. This review, which was commissioned by Biosecurity Queensland in response to the 2015 TR4 outbreak, considers the key epidemiological factors associated with the onset of a Fusarium wilt epidemic. Resistance to TR4, which is mediated by events following entry by the pathogen into the xylem, is not present in any commercially acceptable banana cultivar. Also, there is no effective chemical agent that can be used to manage the disease. Besides prevention, very early recognition and rapid containment of a disease outbreak are necessary to prevent epidemic development. A good understanding of the key factors responsible for disease development is required when devising practical protocols for the destruction of infected plants, treatment of surrounding infested soil, and reduction of inoculum in plant residues and soil.