Many essential processes and interactions on atomic and molecular scales occur at ultrafast timescales. The ability to measure and manipulate ultrashort pulses hold the key to probing and understanding these key processes that physicists, engineers, chemists and biologists study today. Measuring ultrashort pulses means that we measure both the intensity (which is a function of time) and the phase of the pulse in time. Or alternately we might measure spectrum and spectral phase (in the corresponding Fourier domain). In the early 1990's, the invention of FROG opened up the field of ultrashort measurement with it's ability to measure the complete pulse. Since then, there have been a whole host of pulse measurement techniques that have been invented to measure all sorts of ultrashort pulses. However, no variation of FROG nor any other fs pulse measurement technique, for that matter, has yet been able to completely measure arbitrary ultraweak femtosecond light pulses such as those found in nature. In this thesis, we will explore a couple of highly sensitive methods in a quest to measure ultraweak ultrashort pulses. We explore the use of Spectral Interferometry, a known sensitive technique as one possibility. We find that it has certain drawbacks that make it not necessarily suitable to tackle this problem. But in the course of our quest, we find that this technique is highly suitable for measuring 10s of picosecond-long shaped pulses. We discuss a couple of developments which make SI highly practical to use for such shaped pulse-measurements. We also develop a new technique which is a variation of FROG, based on the non-linearity of Difference Frequency Generation and Optical Parametric Amplification, which can amplify pulses as weak as a few hundred attojoules to be able to spectrally resolve them and measure the full intensity and phase of these pulses. This technique offers great potential to measure generalized ultraweak ultrashort pulses.