We demonstrate four experimentally simple methods for measuring very complex ultrashort light pulses. Although each method is comprised of only a few optical elements, they permit the measurement of extremely complex pulses with time-bandwidth products greater than 65,000. First, we demonstrate an extremely simple frequency-resolved-optical gating (GRENOUILLE) device for measuring the intensity and phase of pulses up to ~20ps in length. In order to achieve the required high spectral resolution and large temporal range, it uses a few-cm-thick second harmonic-generation crystal in the shape of a pentagon. This has the additional advantage of reducing the device's total number of components to three. Secondly, we introduce a variation of spectral interferometry (SI) using a virtually imaged phased array and grating spectrometer for measuring long complex ultrashort pulses up to 80 ps in length. Next, we introduce a SI technique for measuring the complete intensity and phase of relatively long and very complex ultrashort pulses. It involves making multiple measurements using SI (in its SEA TADPOLE variation) at numerous delays, measuring many temporal pulselets within the pulse, and concatenating the resulting pulselets. Its spectral resolution is the inverse delay range--many times higher than that of the spectrometer used. The waveforms were measured with ~ fs temporal resolution over a temporal range of ~ns and had time-bandwidth products exceeding 65,000, which to our knowledge is the largest time-bandwidth product ever measured with ~fs temporal resolution. Finally, we demonstrate a single-shot measurement technique that temporally interleaves hundreds of measurements with ~fs temporal resolution. It is another variation of SI for measuring the complete intensity and phase of relatively long and complex ultrashort pulses in a single shot. It uses a grating to introduce a transverse time delay into a reference pulse which gates the unknown pulse by interfering it at the image plane of an imaging spectrometer. It provided ~125 fs temporal resolution and a temporal range of 70 ps using a low-resolution spectrometer.