One challenge of working on hybrid halide perovskites is that the field is moving so rapidly. A second is that there are just too many publications. A third is that many of the older papers use different nomenclature so that it can be difficult to discover them. I started a Mendeley group to track papers, and I think we have done a decent job on the older literature (especially in the key work from the 1980s and 90s). In 2014, there were over 400 publications on CH3NH3PbI3, and there are likely to be over 1000 in 2015 alone, so it is almost impossible to absorb all available information.
From a Web of Science search for "hybrid perovskite OR MAPI OR CH3NH3PbI3 solar cell" with 1564 results - 28th May 2015
Here is a suggested reading list to get started:
1. Dynamic disorder in methylammoniumtrihalogenoplumbates (II) observed by millimeter‐wave spectroscopy (Journal of Chemical Physics, 1987) - Weber reported methylammonium lead iodide in 1978, but the interesting characterisation started here, with the first evidence for disorder due to molecular dipoles.
2. Calorimetric and IR spectroscopic studies of phase transitions in methylammonium trihalogenoplumbates (Journal of Physics and Chemistry of Solids, 1990) - The PhD thesis of Noriko Onoda-Yamamuro is a gold-mine of useful information and careful measurements. It began with a report of the heat capacity and IR spectrum.
3. Conducting tin halides with a layered organic-based perovskite structure (Nature, 1994) - David Mitzi kickstarted interest in the optoelectronic properties of organic-inorganic perovskites beginning here and publishing another 30 or so papers in the following decade.
4. Templating and structural engineering in organic–inorganic perovskites (Dalton Transaction, 2001) - Back to David Mitzi for a review on the chemical and structural diversity of this family of compounds.
5. Organometal Halide Perovskites as Visible-Light Sensitizers for Photovoltaic Cells (JACS, 2009) - The first solar cell from Japan, but note the substantial effort that had been put into developing these materials in advance.
6. Efficient Hybrid Solar Cells Based on Meso-Superstructured Organometal Halide Perovskites (Science, 2012) - The first high-efficiency solid-state solar cell from Henry Snaith FRS and the point in time when the world took notice.
7. Atomistic Origins of High-Performance in Hybrid Halide Perovskite Solar Cells (Nano Letters, 2014) - Essentially a think piece, trying to link experimental observations with theory, and the first suggestion that lattice polarisation is important for the photovoltaic action.
8. Compositional engineering of perovskite materials for high-performance solar cells (Nature, 2015) - Things have progressed since 2012 with solar cells made with a variety of materials in a range of architectures. Sang Il Seok's group hold the record and it is with the complex formulation of meythlammonium/formamidinium - lead - iodide/bromide.
I wouldn't recommend to start with reading about device hysteresis. While the case is almost closed in my opinion, there is no definitive publication yet (just plenty of data and speculation).