The present article is a brief summary of the paper [27], which established new Carleman and observability estimates for a general class of linear wave equations. The main features of these estimates are that (a) they apply to a fully general class of time-dependent domains , with timelike moving boundaries , (b) they apply to linear wave equations in any spatial dimension and with general time-dependent lower-order coefficients , and (c) they allow for smaller time-dependent observation regions than previously obtained from existing Carleman estimate methods. In particular, the results of [27] imply exact controllability for general linear waves, again in settings of time-dependent domains and regions of control.