Inclusion Criteria:
* Female participants only, aged 18 or above
* Participants with advanced solid tumors must have received prior adequate therapy in accordance with local practice for their tumor type and stage of disease, or, in the opinion of the Investigator, a clinical study is the best option for their next treatment based on response to and/or tolerability of prior therapy.
* Metastatic or locoregionally recurrent disease and radiological or objective evidence of progression on or after the last systemic therapy prior to starting IMP.
* ECOG/WHO performance status 0 to 1, and a minimum life expectancy of 12 weeks.
* At least one lesion that is measurable and/or non-measurable, as per RECIST v1.1 and that can be accurately assessed at baseline and is suitable for repeated assessment.
Exclusion Criteria:
* Intervention with any of the following:
* Any cytotoxic chemotherapy, investigational agents, or other anti-cancer drugs for the treatment of advanced cancer from a previous treatment regimen or clinical study within 14 days or 5 half-lives (whichever is shorter) of the first dose of IMP (21 days for myelosuppressive therapies) other than GnRHa (eg, goserelin) and bone-stabilizing agents (eg, zoledronic acid, denosumab).
* Any prescription or non-prescription drugs or other products, including herbal products, known to be moderate or strong inhibitors/inducers of CYP3A4/5 which cannot be discontinued prior to first dose of IMP and withheld throughout the study until 2 weeks after the last dose of study drug.
* Drugs that have a known risk of Torsades de Pointes.
* Radiotherapy with a limited field of radiation for palliation within 1 week of the first dose of IMP.
* Major surgical procedure or significant traumatic injury, within 4 weeks of the first dose of IMP, or an anticipated need for major surgery and/or any surgery requiring general anesthesia during the study.
* Any unresolved toxicities of Grade ≥ 2 from prior anti-cancer therapy (with the exception of alopecia). Participants with stable ≤ Grade 2 neuropathy are eligible.
* Presence of life-threatening metastatic visceral disease, as judged by the Investigator, uncontrolled CNS metastatic disease. Participants with spinal cord compression and/or brain metastases may be enrolled if definitively treated (eg, surgery or radiotherapy) and stable off steroids for at least 4 weeks prior to start of IMP.
* Any evidence of severe or uncontrolled systemic diseases, including uncontrolled hypertension and active bleeding diatheses, or eg, infection requiring IV antibiotic therapy, or active infection including hepatitis B, hepatitis C, and HIV (active viral infection is defined as requiring antiviral therapy; screening for chronic conditions is not required).
* Any of the following cardiac criteria:
* Mean resting QTcF \> 470 msec obtained from a triplicate ECG
* Any clinically important abnormalities in rhythm, conduction, or morphology of resting ECG (eg, complete left bundle branch block, second- and third-degree heart block), or clinically significant sinus pause. Participants with controlled atrial fibrillation can be enrolled.
* Any factors that increase the risk of QTc prolongation or risk of arrhythmic events such as symptomatic heart failure, hypokalemia, congenital long QT syndrome, immediate family history of long QT syndrome or unexplained sudden death at \< 40 years of age. Hypertrophic cardiomyopathy and clinically significant stenotic valve disease.
* LVEF \< 50%, and/or experience of any of the following procedures or conditions in the preceding 6 months: coronary artery bypass graft, angioplasty, vascular stent, myocardial infarction, unstable angina pectoris, congestive heart failure NYHA Grade ≥ 2, cerebrovascular accident, or transient ischemic attack.
* Uncontrolled hypertension.
* Inadequate bone marrow reserve or organ function as demonstrated by relevant laboratory values:
* Refractory nausea and vomiting, uncontrolled chronic gastrointestinal diseases, or previous significant bowel resection that would preclude adequate absorption of IMP(s).
* History of hypersensitivity to active or inactive excipients of AZD8421 or drugs with a similar chemical structure or class to AZD8421.
* Previous treatment with AZD8421 or with any CDK2-selective inhibitor, or protein kinase membrane-associated tyrosine- and threonine-specific cdc2-inhibitory kinase 1 (PKMYT1) inhibitor, or WEE1 inhibitor.
* Currently pregnant (confirmed with positive pregnancy test), breast feeding, or planning to become pregnant. Participants of childbearing potential must agree to use one highly effective contraceptive measure.
