He studied medicine at the Universities of Berlin, Bern and Zurich, earning his doctorate 1861. Among his instructors were Johannes Peter Müller (1801-1858), Ludwig Traube (1818-1876) and Albrecht von Graefe (1828-1870). Later he became a professor of pharmacology at the University of Greifswald, and in 1882, a professor of neurology in Berlin.
Eulenburg is remembered for his written works. His most ambitious work being the multi-volume Real-Encyclopädie der gesammten Heilkunde, which was published in four editions between 1880 and 1914. Later in his career he became interested in the field of sexology, and was co-editor of the journal Zeitschrift für Sexualwissenschaft. In 1902 Eulenburg penned a work on algolagnia, titled Sadismus und Masochismus (Sadism and Masochism). Other principal writings by Eulenburg include:
- Lehrbuch der functionellen Nervenkrankheiten auf Physiologischer Basis. 1871, Page 712: Parry-Romberg syndrome.
- Pathologie des Sympathicus. Prize-winning paper, with Paul Guttmann (1834-1893). Berlin, 1873.
- Handbuch der allgemeinen Therapie und der therapeutischen Methodik. with Simon Samuel (1833-1899). three volumes, Berlin/Vienna, 1898-1899.
- Der Marquis de Sade. Vortrag gehalten im Psychologischen Verein in Berlin. First published in the journal Zukunft on March 25, 1899.
- Lehrbuch der klinischen Untersuchungsmethoden und ihrer Anwendung auf die specielle ärztliche Diagnostik. with Wilhelm Kolle (1868-1935) and Wilhelm Weintraud (1866-1920). Contains a number of treatises on methods of investigating the blood by Kolle and Ernst Grawitz (1860-1911), 1904-05.
Many of his publications dealt with the physiological side of neurology, and he is remembered for research involving the vasomotor centers of the brain. He was the first to describe a rare muscular condition known as paramyotonia congenita, a disorder sometimes referred to as "Eulenburg's disease".
- Bibliography at Who Named It