As SARS-CoV-2 continues to propagate around the world, it is becoming increasingly important to scale up testing. This is necessary both at the individual level, to inform diagnosis, treatment and contract tracing, as well as at the population level to inform policies to control spread of the infection. The gold-standard RT-qPCR test for the virus is relatively expensive and takes time, so combining multiple samples into "pools" that are tested together has emerged as a useful way to test many individuals with less than one test per person. Here, we describe the basic idea behind pooling of samples and different methods for reconstructing the result for each individual from the test of pooled samples. The methods range from simple pooling, where each pool is disjoint from the other, to more complex combinatorial pooling where each sample is split into multiple pools and each pool has a specified combination of samples. We describe efforts to validate these testing methods clinically and the potential advantages of the combinatorial pooling method named Tapestry Pooling that relies on compressed sensing techniques.