Methods of purifying samples are provided that are capable of removing carbonaceous and noncarbonaceous impurities from a sample containing a carbon material having a selected structure. Purification methods are provided for removing residual metal catalyst particles enclosed in multilayer carbonaceous impurities in samples generate by catalytic synthesis methods. Purification methods are provided wherein carbonaceous impurities in a sample are at least partially exfoliated, thereby facilitating subsequent removal of carbonaceous and noncarbonaceous impurities from the sample. Methods of purifying carbon nanotube-containing samples are provided wherein an intercalant is added to the sample and subsequently reacted with an exfoliation initiator to achieve exfoliation of carbonaceous impurities.