Well, in macroeconomics, namely in DSGE modelling, VOXEU has recently published a report on its uses by Central Banks (CBs), and future lines of improvement, which academics have been tackling but still hasn't found its way into CBs policy analysis. There's no space to explain all the new topics, nor do I think it's the intention of this question. So, I'll just enunciate the topics, with some references. More can be found in reading the report. Also, I'll focus on the theoretical considerations, i.e., it's known that, empirically, the the VAR obtained by solving the DSGE model can be considered as misspecified (see here). This is a WP, but you can easily find many articles on this subject, increasingly so since the crisis)
- Financial Frictions (an example)
- Forward Guidance(extending low-rates period), due to the presence of a ZLB (see here; this was already being studied before the crisis.)
- (Incomplete Markets) Heterogeneity across households in
the transmission of monetary and fiscal policy (see here). I would also add firm heterogeneity (example here)
- Systemic fragilities, i.e., economy more prone to crisis due to increasing leverage (an example)
- Allowing for structural (long-run) changes, instead of a simple sequence of short-run shocks, this allows for fluctuations of for example the natural rate of interest (see here and here).
Finally, one critique, with which I agree, and Romer has written very funny and interesting 'WP' on, is the degree of exogeneity, through shocks, that is needed to explain the economy.
Behavioural economics (2017 Nobel prize winner was from this area) may supply us with an answer. It allows to endogenize some of the shocks. Here's an article on VOXEU with many references, and analysis of an example of how it's done.
Edit: To complement Kitsune answer, I find this image from the wikipedia page really good. In a very succint way, it explains the difference between macro and micro prudential perspectives.