Conformal Field Theories (CFTs) in even spacetime dimensions are characterised in part by Weyl anomaly coefficients, the coefficients of curvature invariants in the stress tensor's trace. In particular, these coefficients often appear in various physical observables, such as thermal entropy, stress tensor correlators, universal contributions to entanglement entropy, and more. Many of them also obey powerful non-perturbative constraints, such as c-theorems. What if the CFT has a boundary or defect, however? How do these contribute to the Weyl anomaly? Do their Weyl anomaly coefficients appear in any physical observables, or obey any constraints? In this talk, I will summarise the state of the art and open questions in our understanding of boundary and defect Weyl anomalies, with emphasis on two- and four-dimensional boundaries and defects.