In 1902, Pieter Zeeman shared the Physics Nobel Prize with Hendrik Antoon Lorentz, "in recognition of the extraordinary service they rendered by their researches into the influence of magnetism upon radiation phenomena". In 1952, Felix Bloch and Edward Purcell were awarded the Nobel Prize in Physics for the description of the nuclear magnetic resonance (NMR) experiment, which detects transitions between the "Zeeman levels" of isotopes with non-zero nuclear spin quantum number. Over the years, NMR has then been used in a wide range of fundamental studies in physics. Based on novel concepts and advances in instrumentation and computation, exciting developments in the early 1970s laid the foundations for magnetic resonance imaging (MRI) being today a key technique in medical diagnosis, and for NMR spectroscopy being a widely applied technique in structural biology. Consultation of Albert Einstein's 1905 theory of the Brownian motion of particles suspended in a liquid, which was first reported by the English botanist Robert Brown in 1827, leads to a deeper understanding of NMR with solutions, including body fluids. Here, I will recount these basic concepts with reference to current applications of the NMR principle.