Extensible continuum robots (ECRs) offer distinct advantages over conventional continuum robots due to their ability to enhance workspace adaptability through length adjustments. This makes ECRs particularly promising for applications that require variable lengths involving the manipulation of objects in challenging environments, such as risky, cluttered, or confined. The development of ECRs necessitates careful consideration of mechanical structures, actuation methods, methods of stiffness variability, and control methods. The selection of papers is based on their relevance to ECRs within the period of 2010 to 2023 in the databases of Scopus and Web of Science. Distinguishing itself from other review papers, this paper aims to deliver a comprehensive and critical discussion about the advantages and disadvantages of ECRs concerning their mechanical structures, actuation methods, stiffness variability, and control methods. It is a beneficial resource for researchers and engineers interested in ECRs, providing essential insights to guide future developments in this field. Based on the literature, existing ECRs exhibit an inherent trade-off between flexibility and structural strength due to the absence of systematic design methods. Additionally, there is a lack of intelligent and effective controllers for achieving complex control performance and autonomous stiffness variability.