While ultrasound's cost, safety and interesting contrast mechanisms are of great clinical value, its operatordependence, extensive sonographer training needs, uncompetitive scan times, poor ergonomics and low reproducibility in serial studies limit its proliferation. This paper examines opportunities to solve these problems and increase ultrasound's application space via arrays which conform to the patient's body contours. Progress towards a conformable array maintaining ultrasound's existing feature set has been promising, but a complete system is yet to be demonstrated. The article first outlines the motivation for such arrays, defines design requirements, and describes an ideal design. Next, work on partial hardware realizations of conformable arrays is reviewed, and types of signal processing specific to conformable systems are discussed. Finally, future research directions are envisioned.Operator-independent ultrasound requires large acquisition volumes with voxels isotropic enough to allow post-scan clinical assessment without regard for scanning geometry. Information rate is presented as a useful metric to compare the diagnostic utility of these systems. Two new hardware realizations are described to illustrate progress towards the conformable array goal. An automated breast-scanning design with a matrix receiver using silicon transducers (cMUTs) shows provocative performance in a micro-calcification detection simulation. A reconfigurable matrix array, also using cMUTs, provides volume imaging performance characteristic of a fully-sampled aperture with sufficiently modest interconnect demands to be feasible in a transesophageal echo (TEE) application.