The Taiwanese citizens won't need a visa anymore for the Schengen* area as long as they don't spend more than 90 days there. This decision of the European Union is fully reciprocated by Taiwan, who decided earlier this month to lift the visa requirement for citizens of Romania, Bulgaria and Cyprus, the remaining three EU member states that had not profited from visa free travel to Taiwan before.
The Council of the European Union noted that the visa waiver is implemented despite the fact that the European bloc doesn't recognize Taiwan as a sovereign state and has no diplomatic of formal relations with it. However, the EU has developed regular contacts and cooperation in the fields of economy, trade, research, science and technology, thus becoming the largest foreign investor in Taiwan. This country is the 19th largest trade partner of the EU and Europe is an important destination for Taiwanese citizens.
*/ Wikipedia: The Schengen Area comprises the territories of twenty-five European countries that have implemented the Schengen Agreement signed in the town of Schengen, Luxembourg, in 1985. The Schengen Area operates very much like a single state for international travel purposes with border controls for travellers travelling in and out of the area, but with no internal border controls.