Resonance spectroscopy of light nuclei is discussed with emphasis on the invariant-mass measurements performed with the HiRA detector. For three-body exit channels, we consider the exact conditions necessary such that the decay can be described as either sequential or prompt. However experimentally, we find some cases where the decay is intermediate between these two limits. Finally, two-proton decay from isobaric analog states is discussed.Light nuclei near the drip lines have very few particle-bound levels, with most of their states being in the continuum. Of course those beyond the drip lines have all their levels in the continuum including their ground states. Thus the study of continuum spectroscopy is quite important for these light nuclei. There are many techniques to study these continuum states, however, in this work we will consider just the invariant-mass method and discuss results obtained with the HiRA array [1] at the the National Superconducting Cyclotron Laboratory at Michigan State University and the Texas A&M University cyclotron.It is often assumed that continuum states which are associated with binary exit channels are dominant. However, three-body and high-order exit channels are quite common in light nuclei. For example in the 9 C+ 9 Be reaction at E/A=70 MeV studied with the HiRA detectors [17], we have identified 42 resonances in the continuum which decay into exit channels containing charged particle. These resonances are continuum states in 5,6,7 Li,6,7,8 Be,7,8,9 B, and 8,9,10 C nuclei. Of these, only half were associated with 201 , 0600 (2016) EPJ Web of Conferences