Carbon or activated carbon nanofibers are made from fibrillated nanofibers having a Canadian Standard Freeness of less than about 100, and/or a fiber diameter of less than or equal to about 400 nm. BET surface areas are greater than about 800 m.sup.2/g The fibrillated nanofibers can be made into a precursor paper and subjected to heat treatment to form carbon or activated carbon nanofiber sheets. A method of making is disclosed wherein carbonization occurs at a temperature of less than about 600.degree. C. Activation occurs at temperatures greater than about 875.degree. C. in less than or equal to about 30 minutes in an oxidizing atmosphere. Single step carbonization and activation in an oxidizing atmosphere is also disclosed. The carbon nanofibers or structures made therefrom are useful as filter media providing efficient adsorption and interception of microbiological contaminants due to the microporous carbon nanofiber structure.