The three-day workshop "Physical, Engineering and Biological Limits to Brain Measurements" hosted by the University of Chicago on May 29-31, 2014 will bring together researchers from physics, computational science, biology, and network theory to discuss the foundations of brain science and recent methodological developments in the field. The meeting is inspired in part by ongoing discussions surrounding the BRAIN initiative about the development of new technologies and tools that will help us understand how the brain works and make transformative progress in engineering and medicine. An important part of the discussion will be how to substantially improve the spatial and temporal resolution, miniaturization, numbers of probes or actuators, etc. in brain related experiments. One of the questions that will be discussed is the fundamental limits set by physics (e.g. electrical, optical and wireless methods cannot violate Maxwell's equations), engineering and material science, and from biology (e.g. one cannot over-heat the brain by dissipating too much power). The meeting will bring together practicing experts to have a systematic discussion about these limits, resulting in a written document that can be broadly disseminated to help different parties in understanding the issues, to delineate possible/impossible boundaries and to point to areas requiring further research. This is a small, focused meeting with approximately 30 participants, with a single session attended by the whole group over the meeting period. The meeting will constitute sequential discussions of the different frequency ranges of the Maxwell's equation (EEG/MEG at low frequencies, MRI, wired/wireless, optical, and x-ray), with additional segments on electron microscopy, on a general framework spanning the frequency ranges, and statistics/inverse problems. Young scientists will have the opportunity to interact with the senior investigators in the field.