Through genetic and epigenetic alterations, cancer cells present the immune system with a diversity of antigens or neoantigens, which the organism must distinguish from self. The immune system responds to neoantigens by activating naïve T cells, which mount an anticancer cytotoxic response. T cell activation begins when the T cell receptor (TCR) interacts with the antigen, which is displayed by the major histocompatibility complex (MHC) on antigen-presenting cells (APCs). Subsequently, accessory stimulatory or inhibitory molecules transduce a secondary signal in concert with the TCR/antigen mediated stimulus. These molecules serve to modulate the activation signal’s strength at the immune synapse. Therefore, the activation signal’s optimum amplitude is maintained by a balance between the costimulatory and inhibitory signals. This system comprises the so-called immune checkpoints such as the programmed cell death (PD-1) and Cytotoxic T lymphocyte-associated antigen-4 (CTLA-4) and is crucial for the maintenance of self-tolerance. Cancers often evade the intrinsic anti-tumor activity present in normal physiology primarily by the downregulation of T cell activation. The blockade of the immune checkpoint inhibitors using specific monoclonal antibodies has emerged as a potentially powerful anticancer therapy strategy. Several drugs have been approved mainly for solid tumors. However, it has emerged that there are innate and acquired mechanisms by which resistance is developed against these therapies. Some of these are tumor-intrinsic mechanisms, while others are tumor-extrinsic whereby the microenvironment may have innate or acquired resistance to checkpoint inhibitors. This review article will examine mechanisms by which resistance is mounted against immune checkpoint inhibitors focussing on anti-CTL4-A and anti-PD-1/PD-Ll since drugs targeting these checkpoints are the most developed.