Existentialism has an unusual relationship with different philosophical systems. Most of the time a person will adhere to one system or another, but not both - thus a person might be a Logical Positivist or a Pragmatist, but not both. Existentialism, however, can coexist with many different philosophies.
That co-existence isn't always peaceful because existentialism is likely to be critical of some premises within any given system. At the same time, existentialism can manage to find common ground with those systems that might seem to be the most antagonistic and contradictory to basic existentialist positions.
Existentialism, Marxism, and Communism
In the minds of some there is a close association between existentialist philosophy and Marxist or communist politics. There is some justification for this because one of the most prominent existentialists, Jean-Paul Sartre, was also a Marxist. Nevertheless, there are a number of significant incompatibilities between existentialism and Marxism - incompatibilities which even Sartre had difficulty reconciling.
Existentialism and Humanism
One of Jean-Paul Sartre's most important works was "Existentialism is a Humanism" so are all existentialists humanists? Are all humanists also existentialists? Not necessarily there is a close affinity between existentialism and humanism, but they aren't quite the same thing. Still, Sartre's point is a valid one and deserves to be considered.
Existentialism and Darwinism
Initially, at least, there wouldn't appear to be any particular connection between Charles Darwin's theory of evolution and existentialist philosophy but first impressions can be deceiving. As a matter of fact, there are important connections between the two. This is not to say that there is any sort of causal relationship because existentialism didn't inspire evolution and evolutionary theory didn't help produce existentialism. The relationship between the two is more a matter of spheres of concern and interest.
Aesthetics is the philosophical study of beauty and taste, but few philosophical systems or trends take aesthetics quite as seriously as does existentialism. Aesthetics has traditionally been part of other philosophical pursuits like the investigation of epistemology or ethics. In existentialism, however, art is in some ways the very medium through which philosophy is expressed and communicated.