I have built and designed multichannel MEG instruments and invented for MEG use the minimum-norm estimate (together with Matti Hämäläinen), the signal-space projection, formulas for the forward problem, the channel-capacity measure for comparing sensor arrays, and the triangle phantom. I have developed, together with many excellent students, several transcranial magnetic stimulation (TMS) techniques such as navigated TMS (nTMS), the combined use of TMS and EEG, and multi-locus TMS (mTMS). I am the founder and former CEO of Nexstim Plc, the company that brought nTMS and TMS–EEG to the market. Currently, I lead the development of mTMS and hybrid MEG–MRI systems and apply these technologies for neuroscience and clinical use. Much of my effort is devoted to the development of mathematical methods for improved brain-signal analysis and for data interpretation, often involving work on the bioelectromagnetic inverse problem.