Tyrosine kinase inhibitors (TKIs) have vastly improved long-term outcomes for patients with chronic myeloid leukemia (CML). After imatinib (a first-generation TKI), second- and third-generation TKIs were developed. With five TKIs (imatinib, dasatinib, bosutinib, nilotinib, and ponatinib) targeting BCR::ABL approved in most countries, and with the recent approval of asciminib in the USA, treatment decisions are complex and require assessment of patient-specific factors. Optimal treatment strategies for CML continue to evolve, with an increased focus on achieving deep molecular responses. Using clinically relevant case studies developed by the authors of this review, we discuss three major scenarios from the perspective of international experts. Firstly, this review explores patient-specific characteristics that affect decision-making between first- and second-generation TKIs upon initial diagnosis of CML, including patient comorbidities. Secondly, a thorough assessment of therapeutic options in the event of first-line treatment failure (as defined by National Comprehensive Cancer Network and European LeukemiaNet guidelines) is discussed along with real-world considerations for monitoring optimal responses to TKI therapy. Thirdly, this review illustrates the considerations and importance of achieving treatment-free remission as a treatment goal. Due to the timing of the writing, this review addresses global challenges commonly faced by hematologists treating patients with CML during the COVID-19 pandemic. Lastly, as new treatment approaches continue to be explored in CML, this review also discusses the advent of newer therapies such as asciminib. This article may be a useful reference for physicians treating patients with CML with second-generation TKIs and, as it is focused on the physicians' international and personal experiences, may give insight into alternative approaches not previously considered.