Anyone who works remotely will generally pay taxes to the state in which the work is performed (the "physical presence" rule). Employers will generally also pay taxes on wages paid to these workers to the same state, even if the employer has no physical presence in that state.
Companies must register with the appropriate tax agencies in each state where at least one individual is working, even for remote workers.
For example, let's assume we have someone who is employed by a company located in Massachusetts, but lives and works in California.
The individual should be taxed in California.
The company should register with the proper tax agencies in the state of California.
In the rare case that the remote worker happens to live and work in two different states that have reciprocal agreements, they may choose to file a Certificate of Non-residency to be exempted from paying taxes in the work state and instead pay taxes in their home state.
New York, Nebraska, Pennsylvania, Delaware, and New Jersey may require that workers are taxed based on their employer's location. For remote workers, this means that they would be subject to income tax for both the state that they reside in and by their employer's state if the employer is located in New York, Nebraska, Pennsylvania, Delaware, or New Jersey.