Recent advances in the construction of Hadamard matrices

In the past few years exciting new discoveries have been made in constructing Hadamard matrices. These discoveries have been centred in two ideas: (i) the construction of Baumert-Hall arrays by utilizing a construction of L. R. Welch, and (ii) finding suitable matrices to put into these arrays. We discuss these results, many of which are due to Richard J. Turyn or the author.