How is encryption broken today? There are often articles in the news that state that a certain country or hacker has been able to decrypt/hack highly protected systems: Some examples are the Lockheed Martin RQ-170 Sentinel that was downed in Iran and later said to be partly reverse engineered by China or the Snowden files that might have been hacked by Russia and China. There are plenty of other examples. 

My question is now the following: How could this have been done considering the fact that a brute-force method would certainly not work because of the encryption strength and leaving other non-technical aspects like spies etc. out of consideration.
Modern encryption can be broken in practice even when the algorithms are theoretically secure. There are a variety of ways this can happen:


Side channel analysis could have played a part.


The accepted answer to the linked question is excellent and provides some very good examples.

Exploitation of implementation bugs could have played a part.
Malware presence on the machine more or less negates any benefits of encryption, as advanced enough malware can simply watch and even modify anything/everything that you do.
Users may simply be coerced into surrendering the password which is used to derive their encryption keys.


More about Side Channels


  General classes of side channel attack include:
  
  
  Cache attack — attacks based on attacker's ability to monitor cache accesses made by the victim in a shared physical system as in virtualized environment or a type of cloud service.
  Timing attack — attacks based on measuring how much time various computations take to perform.
  Power-monitoring attack — attacks that make use of varying power consumption by the hardware during computation.
  Electromagnetic attack — attacks based on leaked electromagnetic radiation, which can directly provide plaintexts and other information. Such measurements can be used to infer cryptographic keys using techniques equivalent to those in power analysis or can be used in non-cryptographic attacks, e.g. TEMPEST (aka van Eck phreaking or radiation monitoring) attacks.
  Acoustic cryptanalysis — attacks that exploit sound produced during a computation (rather like power analysis).
  Differential fault analysis — in which secrets are discovered by introducing faults in a computation.
  Data remanence — in which sensitive data are read after supposedly having been deleted.
  Row hammer — in which off-limits memory can be changed by accessing adjacent memory.
  Optical - in which secrets and sensitive data can be read by visual recording using a high resolution camera, or other devices that have such capabilities.