Welch's method has been my go-to algorithm for computing power spectral density (PSD) of evenly-sampled timeseries. I noticed that there are many other methods for computing PSD. For example, in Matlab I see:

• PSD using Burg method
• PSD using covariance method
• PSD using periodogram
• PSD using modified covariance method
• PSD using multitaper method (MTM)
• PSD using Welch's method
• PSD using Yule-Walker AR method
• Spectrogram using short-time Fourier transform
• Spectral estimation

What are the advantages of these various methods? As a practical question, when would I want to use something other than Welch's method?