Young massive clusters (YMCs) differ markedly from old globular clusters in featuring extended, rather than tidally truncated, envelopes. Their projected- luminosity profiles are well fit by Elson-Fall-Freeman (EFF) models with core radii of 0.3 pc < r_c < 8 pc and power-law envelopes of negative exponent 2 < gamma < 3.8. These envelopes form within the first few 10^6 yr and last ~10^8 to 10^9.5 yr, depending on the environment. Many young massive clusters show clumpy substructure that may accelerate their initial relaxation. The cores of Magellanic-Cloud clusters show universal expansion from r_c < 1 pc at birth to r_c = 2 - 3 pc after 10^8 yr, but then seem to evolve along two bifurcating branches in a r_c-log(age) diagram. The lower branch can be explained by mass-loss driven core expansion during the first 10^9 yr, followed by slow core contraction and the onset of core collapse due to evaporation. The upper branch, which shows continued core expansion proportional to logarithmic age, remains unexplained. There is strong evidence for rapid mass segregation in young clusters, yet little evidence for top-heavy IMFs or primordial mass segregation. Finally, YMCs show similar structure throughout the Local Group and as far away as we can resolve them (<~20 Mpc).