The definition of a computer crime varies greatly from country to country and state to state but generally includes:
Data theft. Financial account info, personally identifiable information (PII), inttellectual property, trade secrets
Denial of service (DoS)
Data alteration. Fraud
System takeover. Command and control, botnet, army of zombies
Social engineering. Phishing, scams
Dumpster diving. Not exactly a crime, but losses still incurred due to exposure of sensitive information, intellectual property
A computer can become involved in a computer crime as the target, as the attack, and as a support system for the crime.
Law systems around the world include codified law systems, common law systems, customary law systems, ...