Nucleic acid testing (NAT) designate any molecular approach used for the detection, identification, and characterization of pathogenic microorganisms, enabling the rapid, specific, and sensitive diagnostic of infectious diseases, such as tuberculosis. These assays have been widely used since the 90s of the last century in human clinical laboratories and, subsequently, also in veterinary diagnostics. Most NAT strategies are based in the polymerase chain reaction (PCR) and its several enhancements and variations. From the conventional PCR, real-time PCR and its combinations, isothermal DNA amplification, to the nanotechnologies, here we review how the NAT assays have been applied to decipher if and which member of the Mycobacterium tuberculosis complex is present in a clinical sample. Recent advances in DNA sequencing also brought new challenges and have made possible to generate rapidly and at a low cost, large amounts of sequence data. This revolution with the high-throughput sequencing (HTS) technologies makes whole genome sequencing (WGS) and metagenomics the trendiest NAT strategies, today. The ranking of NAT techniques in the field of clinical diagnostics is rising, and we provide a SWOT (Strengths, Weaknesses, Opportunities, and Threats) analysis with our view of the use of molecular diagnostics for detecting tuberculosis in veterinary laboratories, notwithstanding the gold standard being still the classical culture of the agent. The complementary use of both classical and molecular diagnostics approaches is recommended to speed the diagnostic, enabling a fast decision by competent authorities and rapid tackling of the disease.