The International Academy of Cytology (IAC) gathered together a group of cytopathologists expert in breast cytology who, working with clinicians expert in breast diagnostics and management, have developed the IAC Yokohama System for Reporting Breast Fine-Needle Aspiration Biopsy (FNAB) Cytology. The project was initiated with the first cytopathology group meeting in Yokohama at the 2016 International Congress of Cytology. This IAC Yokohama System defines five categories for reporting breast cytology, each with a clear descriptive term for the category, a definition, a risk of malignancy (ROM) and a suggested management algorithm. The key diagnostic cytopathology features of each of the lesions within each category will be presented more fully in a subsequent atlas. The System emphasizes that the crucial requirements for diagnostic breast FNAB cytology are a high standard for the performance of the FNAB and for the making of direct smears, and well-trained experienced cytopathologists to interpret the material. The performance indicators of breast FNAB, including specificity and sensitivity, negative predictive value, positive predictive value and ROM stated in this article have been derived from the recent literature. The current practice of breast FNAB has evolved with the increasing use of ultrasound guidance and rapid on-site evaluation. Two recent publications have shown a range of ROM for the insufficient/inadequate category of 2.6–4.8%, benign 1.4–2.3%, atypical 13–15.7%, suspicious of malignancy 84.6–97.1%, and malignant 99.0–100%. The management algorithm in the System provides options because there are variations in the management of breast lesions using FNAB and core-needle biopsy in those countries utilizing the “triple test” of clinical, imaging, and FNAB assessment, and also variations in the availability of CNB and imaging in low- and middle-income countries. The System will stimulate further discussion and research, particularly in the cytological diagnostic features of specific lesions within each category and in management recommendations. This will lead to continuing improvements in the care of patients with breast lesions and possible modifications to the IAC Yokohama System.