Biological drugs with gene and cell therapy potentials, including natural or rationally created biomacromolecules, recombinant proteins/enzymes, gene-carrying DNA/RNA fragments, oncolytic viruses, plasmid and viral vectors or other gene delivering vehicles with specific therapeutic genes and gene manipulation tools, and genetically modified and reprogrammed human cells comprise a large fraction of drug development candidates in modern precision and regeneration medicine. These drugs have displayed unique capabilities in treating patients with previously incurable diseases. However, most of the drug preparations have complex multimolecular structures and require specific biomanufacturing systems and many other additional biological active materials for drug synthesis, cell expansion, and production enhancement. Thus, the final products would have to be subjected to sequential extensive purification processes to exclude impurities and to concentrate the drug products after manufacturing. The quality evaluation for each drug product is an individualized process and must be specifically designed and performed according to the characteristics of the drug and its manufacturing and purification methods. Some of the Quality Control (QC) assays may be very costly and time-consuming, frequently with inconsistent test results from batch-to-batch. This review focuses on QC assessment strategy development for common gene and cell therapy drugs which use prokaryotic or eukaryotic cells for manufacturing or cell factories for in vitro expansions, especially for drug identification and concentration determination, impurity detection and quantification, drug potency, stability, and safety evaluations; and discusses some key issues for drug quality assessments in different categories and emphasizes the importance of individualized QC strategy design.