Estonians and other EU-citizens:

It is not required for Estonians or other EU-citizens to get a visa for a business or tourist trip to Germany. However, they must at all times during their stay in Germany be able to identify themselves with a valid passport or a national ID-card. Please note that for Estonian citizens only the passport and the national ID card are valid travel documents for trips to Germany.

Third-Country nationals:

Foreigners with a valid Estonian residence permit and a valid passport or travel document that is acknowledged by German authorities do not need a visa for tourist trips to Germany that do not exceed 90 days. You need to bring your passport and residence permit card.
Non EU citizens can only travel within the EU with a valid passport and a valid residence permit. If your residence permit for Estonia has expired, you have to apply for an extension with the Estonian migration service. Until a decision has been made, you are unfortunately not allowed to travel to Germany. For questions regarding travel plans and your future residence within the Schengen area, please turn to the Estonian authorities. The German Embassy cannot help you in this matter.