Despite the emergence of various cancer treatments, such as surgery, chemotherapy, radiotherapy, and immunotherapy, their use remains restricted owing to their limited tumor elimination efficacy and side effects. The use of nanoassemblies as delivery systems in nanomedicine for tumor diagnosis and therapy is flourishing. These nanoassemblies can be designed to have various shapes, sizes, and surface charges to meet the requirements of different applications. It is crucial for nanoassemblies to have enhanced delivery of payloads while inducing minimal to no toxicity to healthy tissues. In this review, stimuli-responsive nanoassemblies capable of combating the tumor microenvironment (TME) are discussed. First, various TME characteristics, such as hypoxia, oxidoreduction, adenosine triphosphate (ATP) elevation, and acidic TME, are described. Subsequently, the unique characteristics of the vascular and stromal TME are differentiated, and multiple barriers that have to be overcome are discussed. Furthermore, strategies to overcome these barriers for successful drug delivery to the targeted site are reviewed and summarized. In conclusion, the possible challenges and prospects of using these nanoassemblies for tumor-targeted delivery are discussed. This review aims at inspiring researchers to develop stimuli-responsive nanoassemblies for tumor-targeted delivery for clinical applications.