Persisters are transiently tolerant variants that allow populations to avoid eradication by antibiotic treatment. Their antibiotic tolerance is non-genetic, not inheritable and results from a phenotypic switch from the normal, sensitive cell type to the tolerant, persister state. Here we give a comprehensive overview on bacterial persistence. We first define persistence, summarize the various aspects of persister physiology and show their heterogeneous nature. We then focus on the role of key cellular processes and mechanisms controlling the formation of a subpopulation of tolerant cells. Being a prime example of a risk-spreading strategy, we next discuss the eco-evolutionary aspects of persistence, e.g. how persistence evolves in the face of treatment with antibiotics. Finally, we illustrate the clinical importance of persisters, as persistence is worsening the worldwide antibiotic crisis by prolonging antibiotic treatment, causing therapy failure or catalyzing the development of genetically encoded antibiotic resistance. A better understanding of this phenotype is critical in our fight against pathogenic bacteria and to obtain a better outlook on future therapies.