Independent of the source of data, the integration of event streams into an Enterprise Architecture gets more and more important in the world of sensors, social media streams and Internet of Things. Events have to be accepted quickly and reliably, they have to be distributed and analyzed, often with many consumers or systems interested in all or part of the events. Storing such huge event streams into HDFS or a NoSQL datastore is feasible and not such a challenge anymore. But if you want to be able to react fast, with minimal latency, you can not afford to first store the data and doing the analysis/analytics later. You have to be able to include part of your analytics right after you consume the data streams. Products for doing event processing, such as Oracle Event Processing or Esper, are available for quite a long time and used to be called Complex Event Processing (CEP). In the past few years, another family of products appeared, mostly out of the Big Data Technology space, called Stream Processing or Streaming Analytics. These are mostly open source products/frameworks such as Apache Storm, Spark Streaming, Flink, Kafka Streams as well as supporting infrastructures such as Apache Kafka. In this talk I will present the theoretical foundations for Stream Processing, discuss the core properties a Stream Processing platform should provide and highlight what differences you might find between the more traditional CEP and the more modern Stream Processing solutions.