We briefly review the recent progress in passively mode-locked fiber lasers (PMLFLs) based on semiconductor saturable absorber mirrors (SESAMs) and discuss the detailed characterization of a SESAM-based, passively mode-locked erbium-doped fiber (EDF) laser operating in the 1.5-${mu}m$ spectral range for various configurations. A simple and compact design of the laser cavity enables the PMLFL to generate either femtosecond or wavelength-tunable picosecond pulses with high stability as the intra-cavity filtering method is altered. All the cavities investigated in our experiments present self-starting, continuous-wave mode-locking with no Q-switching instabilities. The excellent stability of the source eventually enables the wavelength-tunable PMLFL to be used as a master oscillator for a power-amplifier source based on a large-core EDF, generating picosecond pulses of >10-kW peak power and >100-nJ pulse energy.