conductivity. [1] Following the discovery of SnO 2 with a similar unique combination of properties, [2] several patents were filed in the 1940s to employ TCOs as antistatic coatings and transparent heaters-long before the discovery of the now well-known Sn-doped In 2 O 3 (ITO) and Al-doped ZnO, [3] widely employed as flat panel display electrodes in the past decades. Despite great technological demand for TCOs [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and extensive experimental efforts to improve the conductivity via impurity doping, [21,22] to tune the work function and carrier concentration via cation composition, [23][24][25][26][27][28] to achieve two-dimensional transport via heterointerfaces, [29] and to p-dope the oxides toward active layers of transparent electronics, [30][31][32] theoretical understanding of these fascinating materials has lagged behind significantly. The first electronic band structure of ITO was calculated in 2001; [33] the role of native defects in prototype TCOs was understood after 2002; [34][35][36][37] the properties of multi-cation TCOs were first considered in 2004 [37][38][39][40][41][42] followed by modeling of novel TCO hosts [43,44] and spin-dependent transport in transition-metal-doped TCOs; [45] the nature of the band gap in In 2 O 3 was clarified in 2008; [46] and a first highthroughput search for p-type TCOs was performed in 2013. [47] Complex oxides that consist of multiple post-transition metals, such as InGaZnO 4 , have recently become competitive with silicon as the active transistor layer to drive arrays of pixels in large area displays. [9,[13][14][15][16][17][18][19]24] As the billion-dollar display industry moves forward, the amorphous phase of the complex oxides is favored both for flexible and high-resolution display applications. [13][14][15][16][48][49][50][51][52][53][54][55][56][57][58][59] The unique properties of AOSs were first demonstrated in 1990, [60] and the research area has been growing exponentially since then. Unlike Si-based semiconductors, AOSs were shown to exhibit optical, electrical, thermal, and mechanical properties that are comparable or even superior to those possessed by their crystalline counterparts. [48][49][50][51][52][53][54][55][56][57][58] Table 1 summarizes the key physical properties of best-performing crystalline TCOs and AOSs; the differences (or the lack thereof) between the two will be discussed in detail in the respective sections below.