Prosthetic heart valve devices with tethered anchors and associated systems and methods are disclosed herein. A heart valve device configured in accordance with embodiments of the present technology can include, for example, a valve support for carrying a prosthetic valve. The valve support can be configured to be implanted at an annulus of a native mitral valve. The device can further include at least one elongated flexible member extending from the valve support in a ventricular direction, and an anchor coupled to the valve support via the elongated flexible member. The anchor can be shaped to wrap around an exterior area of an apical portion of the heart. In addition, the anchor can inhibit retrograde migration of the valve support.