Acquired genetic mutations in hematopoietic stem or progenitor cells can lead to clonal expansion and imbalanced blood cell production. Clonal hematopoiesis is exceptionally common with human aging, confers a risk of evolution to overt hematologic malignancy, and also increases all-cause mortality and the risk of cardiovascular disease. The degree of risk depends on the specific mutation, number of mutations, mutant allele burden, and concomitant non-genetic risk factors (e.g., hypertension or cigarette smoking). People with clonal hematopoiesis may come to clinical attention in a variety of ways, including during the evaluation of a possible hematologic malignancy, as an incidental discovery during molecular analysis of a non-hematological neoplasm, after hematopoietic cell transplant, or as a result of germline testing for inherited variants. Even though the risk of clonal progression or a cardiovascular event in an individual patient may be low, the possibility of future clinical consequences may contribute to uncertainty and worry, since it is not yet known how to modify these risks. This review summarizes clinical considerations for patients with clonal hematopoiesis, including important points for hematologists to consider discussing with affected persons - individuals who may understandably be anxious about having a mutation in their blood that predisposes them to develop malignancy, but which is statistically more likely to result in a myocardial infarction or stroke. The increasing frequency with which people with clonal hematopoiesis are discovered and the need for counseling these patients is driving many institutions to create specialized clinics; we describe our own experience with forming such clinics.