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.It is also argued that the downside of the early RBC and NKE models was that they just didn't work. These two initially competing strains of business cycle research have gradually merged over time. More recently things have gotten better for a number of reasons.
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.
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.Update: The visible hand in economics asks What is modern business cycle theory.