There are of course many approaches to data storage and analysis. There's no single approach. However, here's what I have seen. It's a two step process.
First, get the data. Ingesting and storing data is done up front often by a dedicated group of software engineers (Quantopian has a team for this). If one has a small quant group (or even just an individual) this still is a separate step. This isn't typically considered a 'quant job' but rather a 'data engineer'. There are a number of platforms but common ones are 1) relational databases 2) flat files, and more recently 3) a number of cloud based solutions such as AWS Data Lakes . One aspect of financial data is that it's typically time series and typically fetched across contiguous dates. Relational databases, while ubiquitous and mature, are designed to fetch random pieces of data. They aren't generally optimized to fetch streams of contiguous data by date.
Second, analyze and use the data. Once data is stored and organized it's manipulated by 'quants'. Python is a widely used platform for this step (Quantopian of course is based on Python so I'm biased). The key feature which has made this popular in fintech is its extensibility. Basic Python (that one would learn in a Python 101 class) by itself isn't all that helpful. The power to easily analyze large chunks of data comes from using packages such as Pandas, NumPy, SciPy, and Matplotlib (for visualization). Those are the tools that quite a few quants use on a day to day basis.
Just my 2-cents.
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