Four areas of research in architectural acoustics in which significant advances have been achieved recently are discussed. 1. Reliable determination of subjective preference of concert hall acoustics by means of faithful (three-dimensional) reproduction of music recorded in concert halls with an acoustically realistic dummy head: The main new result, based both on real halls and digital simulations of halls, is that interaural dissimilarity should be high for high preference. This finding implies the need for more lateral diffusion in concert halls. 2. Effective methods for increasing sound diffusion: In modern wide halls with low ceilings, the two ear signals for a listener on the main floor tend to be very similar owing to strong ceiling reflections (relative to the reflections from the side walls). Thus, ceiling structures for scattering sound laterally should improve concert hall quality. Such structures, based on two number-theoretic principles (quadratic residues and primitive roots) are discussed. 3. Proper calculation of reverberation time: Sound decay rates and sound energy fluxes, based on ray theory, are given by two integral equations. Their solution, recently achieved, shows variations of decay rates by as much as 48% depending only on absorber location!(The Sabine and Eyring formulas, of course, predict no such variations and consequently lead to costly errors.) 4. Making meaningful measurements in acoustic enclosures: A recently discovered fast inverse for measurements using maximum-length pseudo-random noise is described. Some implications for making measurements with music during ongoing performance, are discussed.