Current Patent Law
The first time that Europe decided not to allow software patents was in 1974 when the European Patent Convention was ratified.The European Patent Convention (EPC) of 1974 is not an EU-related agreement. It is a separate multi-national treaty that was initially ratified in 1974, and other countries became members of the European Patent Organisation over time. The European Patent Office was formed under the EPC, and the member states of the European Patent Organisation (basically the governing body of the European Patent Office) incorporated the principles of the EPC into their national patent laws.
Article 52 of the EPC defines patentability quite clearly. You can find the full text of that article here. It states in its 2nd paragraph that "mathematical methods" and "programs for computers" are not patentable inventions. In paragraph 3, it then states that this exclusion of patentability "relates to such subject-matter or activities as such."
The whole problem of software patents in Europe arose from the way in which the patent system increasingly interpreted the two little words "as such". Common sense wouldn't attach much importance to that. Obviously there are, with or without that paragraph, various technical inventions in which mathematical methods or algorithms may perform an auxiliary role. The insatiable patent system, however, clutched to those two words like to a straw. They said: "This means that we just have to come up with a technical alibi and then we can patent software by saying that we don't patent software as such. We patent software by portraying it as an integral part of a technical invention."
It's beyond imagination to what extent the European Patent Office has applied that approach. For instance, to them a progress bar on a computer screen is a technical invention and not software. How do they justify that classification? They say that the progress bar makes more efficient use of a technical resource or device, and a screen is a technical device with a limited number of pixels.
They coined that monstrous term of "computer-implemented inventions". They trained patent attorneys to present pure software concepts and mathematics in a way that is consistent with the strange logic of the European Patent Office. Now they and their political friends, and large corporations with their special interests, want to make sure that this dubious interpretation of the European Patent Office can not be overruled by national courts any more, who are often take more restrictive approach. By creating a single, centralized court at the European Patent Office that would have the final decisions, national courts will be silenced.
Don't be misled by the story of "computer-implemented inventions". Contrary to what you'll be told, there is nothing truly technical about most of them. The threshold for that technical alibi is extremely low. Patent attorneys have the typical wordings and drawings (of computer networks and similar "technical configurations") on their computers and use them again and again to obtain software patents. You can read more about the misleading nature of the term "computer-implemented inventions" here. Or if you're mentally prepared to see a little shop of horrors of 20 such "computer-implemented inventions", such as a shopping cart or the concept of ordering via a mobile phone, then take a look at this.