Immune checkpoint inhibitors appear to be one of the most promising immunotherapies with significant clinical benefits and durable responses in multiple tumor types. A heterogeneity of responses appears in patients receiving checkpoint blockade, including pseudoprogression where the tumor burden or number of tumor lesions increases initially before decreasing. Another special response observed after checkpoint blockade is hyperprogression, a phenomenon reflecting a very rapid tumor progression following immunotherapy, suggesting that checkpoint blockade could impact detrimentally on a small subset of patients. As immunotherapeutics, especially anti-PD-1/PD-L1 agents, become more widely available, evaluating the efficacy of these novel drugs poses a major challenge to clinicians, who aim to avoid either premature withdrawal of the treatment or prolonging ineffective treatment. Although the mechanism and recognition of pseudoprogression have gradually come to light, the incidence, basis, identification and predictive biomarkers of hyperprogression have been largely unknown, and this review documents the existing research findings and points out the areas where further studies are badly needed.