Modern business cycle theory is built around two strikingly original ideas.
First was the audacious idea that the observed business cycle was not a problem but actually Pareto optimal in the sense that the economy was fully competitive, there were no externalities, and all agents were operating on their supply curves at all points in the cycle. This was the original real business cycle (RBC) theory of Prescott that the cycle was just the result of optimal responses to real shocks.
Second was the insight that the macroeconomics of imperfect competition was fundamentally different than that of perfect competition. Specifically, if firms face a downward sloping demand curve, then deviations from their optimal price are not infinitely costly and perhaps small nominal barriers to changing prices (menu costs) could deter rational profit maximizing firms from always immediately adjusting their price in response to a nominal disturbance. This was the original new Keynesian economics (NKE) of Mankiw and Blanchard & Kiyatoki.
Early RBC theory just didn't work. Even with a low bar for evidence (matching selected raw moments and a lot of free parameters), it didn't fit the data. Early NKE didn't work either. Ball and Romer showed that menu costs alone would not be sufficient to prevent rapid price adjustments and argued that some real rigidities were also needed. But real rigidities can kind of be a hard thing to theoretically justify.
These two initially competing strains of business cycle research then gradually merged over time with the methods of RBC being applied to the models of NKE. The acronym du jour is DSGE (for Dynamic Stochastic General Equilibrium). However, much of the theoretical purity and the goal of having models built from individual optimizing was lost as more and more ad hoc types of constraints and rigidities were built in to try and get the models to better match the data. Also the idea of state dependent price changes that characterize the theoretical models is often "proxied" by the Calvo rule which simply gives a fixed probability that a firm will be allowed to change its price in a period.
I really thought this literature was going to fade away (as the number of ad hoc ad ons to the models was approaching infinity), but there have been some great new advances recently. First is the work estimating the models rather than calibrating them, often using Bayesian computational methods, and testing the models in a more rigorous way. Second is the new attention being paid to regime switches in monetary policy. Third is work that allows for real state dependent pricing in the model. Fourth are new theoretical ideas being applied, like the paper I referenced yesterday that explores the public good aspect of a firm's price change.
It's a great time to be a macroeconomist!