Conventional CD8+ memory T cells develop upon stimulation with foreign antigen and provide increased protection upon re-challenge. Over the past two decades, new subsets of CD8+ T cells have been identified that acquire memory features independently of antigen exposure. These antigen-inexperienced memory T cells (TAIM) are described under several names including innate memory, virtual memory, and memory phenotype. TAIM cells exhibit characteristics of conventional or true memory cells, including antigen-specific responses. In addition, they show responsiveness to innate stimuli and have been suggested to provide additional levels of protection toward infections and cancer. Here, we discuss the current understanding of TAIM cells, focusing on extrinsic and intrinsic molecular conditions that favor their development, their molecular definitions and immunological properties, as well as their transcriptional and epigenetic regulation.