This paper analyses the relationship between the drop in traditional crimes in Western highly industrialized societies and the evolution of cybercrime. It includes a review of the criminological debate on the crime drop, which shows that the exchanges between researchers allowed clarifying its extent and limits, but without reaching agreement about its causes and seldom taking into account the trends in cyber-related offences. The paper also reviews the data available on the latter and arrives to the conclusion that European police statistics rarely include them and, when they do, the available data do not allow establishing trends nor conducting comparisons across countries. The difficulties related to the recording of such crimes are discussed and a proposal for a tripartite classification of crimes that distinguishes between offline, online, and hybrid crimes is advanced, together with suggestions on the statistical counting rules that could be applied to measure the frequency of cyber-related offences. Finally, a review of the available victimization surveys shows that cybercrime could currently represent between one-third and half of the crimes committed in a country. Accordingly, the authors consider that the rise of online and hybrid crimes have contributed to the drop of offline crimes. This is a consequence of the development of the Internet, which changed the lifestyle and routine activities of the population, and opened a breach in traditional police-based crime prevention strategies. The new scenario helped consolidating the private security market and, indirectly, led the companies involved to hold a strategic data collection, which could be used to study cybercrime.