Cancer remains one of the leading causes of death in the world. For a number of neoplasms, the efficiency of conventional chemo- and radiation therapies is insufficient because of drug resistance and marked toxicity. Plasmonic photothermal therapy (PPT) using local hyperthermia induced by gold nanoparticles (AuNPs) has recently been extensively explored in tumor treatment. However, despite attractive promises, the current PPT status is limited by laboratory experiments, academic papers, and only a few preclinical studies. Unfortunately, most nanoformulations still share a similar fate: great laboratory promises and fair preclinical trials. This review discusses the current challenges and prospects of plasmonic nanomedicine based on PPT and photodynamic therapy (PDT). We start with consideration of the fundamental principles underlying plasmonic properties of AuNPs to tune their plasmon resonance for the desired NIR-I, NIR-2, and SWIR optical windows. The basic principles for simulation of optical cross-sections and plasmonic heating under CW and pulsed irradiation are discussed. Then, we consider the state-of-the-art methods for wet chemical synthesis of the most popular PPPT AuNPs such as silica/gold nanoshells, Au nanostars, nanorods, and nanocages. The photothermal efficiencies of these nanoparticles are compared, and their applications to current nanomedicine are shortly discussed. In a separate section, we discuss the fabrication of gold and other nanoparticles by the pulsed laser ablation in liquid method. The second part of the review is devoted to our recent experimental results on laser-activated interaction of AuNPs with tumor and healthy tissues and current achievements of other research groups in this application area. The unresolved issues of PPT are the significant accumulation of AuNPs in the organs of the mononuclear phagocyte system, causing potential toxic effects of nanoparticles, and the possibility of tumor recurrence due to the presence of survived tumor cells. The prospective ways of solving these problems are discussed, including developing combined antitumor therapy based on combined PPT and PDT. In the conclusion section, we summarize the most urgent needs of current PPT-based nanomedicine.