AKI affects approximately 13.3 million people around the world each year, causing CKD and/or mortality. The mammalian kidney cannot generate new nephrons after postnatal renal damage and regenerative therapies for AKI are not available. Human kidney tissue culture systems can complement animal models of AKI and/or address some of their limitations. Donor-derived somatic cells, such as renal tubule epithelial cells or cell lines (RPTEC/hTERT, ciPTEC, HK-2, Nki-2, and CIHP-1), have been used for decades to permit drug toxicity screening and studies into potential AKI mechanisms. However, tubule cell lines do not fully recapitulate tubular epithelial cell properties in situ when grown under classic tissue culture conditions. Improving tissue culture models of AKI would increase our understanding of the mechanisms, leading to new therapeutics. Human pluripotent stem cells (hPSCs) can be differentiated into kidney organoids and various renal cell types. Injury to human kidney organoids results in renal cell-type crosstalk and upregulation of kidney injury biomarkers that are difficult to induce in primary tubule cell cultures. However, current protocols produce kidney organoids that are not mature and contain off-target cell types. Promising bioengineering techniques, such as bioprinting and "kidney-on-a-chip" methods, as applied to kidney nephrotoxicity modeling advantages and limitations are discussed. This review explores the mechanisms and detection of AKI in tissue culture, with an emphasis on bioengineered approaches such as human kidney organoid models.