While the market's big run-up in 2020 may have some investors convinced that all the well-known tech stocks have been overbought, a closer look reveals a different story. Some of the best growth stocks that have appreciated significantly during the recent bull market are deserving of their premium prices. Even more, some arguably remain attractive.

Two growth stocks that continue to look like buys are Twilio (NYSE:TWLO) and Facebook (NASDAQ:FB). Twilio's business is growing incredibly fast, fueled by impressive customer metrics. Meanwhile, Facebook has morphed into one of the tech sector's most impressive cash cows.

Here's closer a look at both of these companies.

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1. Twilio

Cloud-based communication specialist Twilio may command an expensive-looking valuation. It boasts approximately a $70 billion market capitalization despite generating less than $2 billion in trailing-12-month revenue. But the company's financials easily live up to this premium price -- and Twilio's just-released fourth-quarter results drive this home.

On Wednesday afternoon, Twilio reported fourth-quarter revenue of $548.1 million, up 65% year over year. This was a significant acceleration from 52% growth in the third quarter of 2020. Even when backing out the $23 million of incremental Q4 revenue the company generated from a recent acquisition, Twilio's top line grew 59% year over year. Further highlighting the company's momentum, this marked Twilio's second quarter in a row of accelerating growth. The tech company is capitalizing on a "generational opportunity," said Twilio co-founder and CEO Jeff Lawson.

Fueling Twilio's momentum is both strong customer growth and impressive improvement in spend from existing customers. Customers totaled 221,000, up from 179,000 in the year-ago quarter -- and spend from customers who were with Twilio a year ago increased 39%.

While Twilio stock is trading sharply higher on its fourth-quarter report, there's likely still plenty of room for it to run (albeit probably with some huge volatility along the way) over the long haul.

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2. Facebook

Though Facebook's 21% year-over-year revenue growth in 2020 certainly isn't as impressive as Twilio's 55% top-line growth last year, the stock has a particularly attractive valuation. On $85 billion of revenue in 2020, Facebook generated $29 billion of net income, and that net income was up from less than $19 billion in 2019.

Moreover, the social network's business is supported by one of the most powerful network effects in the world. Across its family of social networks -- Facebook, Messenger, WhatsApp, and Instagram -- the company has 2.6 billion daily active users. And this user base is still growing nicely. In 2020, these daily active users were up 15% year over year.

Despite its attractive profitability profile and its strong growth, Facebook trades at just 27 times earnings. While management does expect to face some ad targeting challenges in 2021 and beyond, Facebook's lucrative business model and its engaged user base give the social network a firm foundation to find ways to grow revenue and profits even in an evolving digital advertising landscape.

Both of these stocks look attractive at their current prices, presenting investors an opportunity to buy some promising growth stocks -- even after 2020's big run higher.

This article represents the opinion of the writer, who may disagree with the “official” recommendation position of a Motley Fool premium advisory service. We’re motley! Questioning an investing thesis -- even one of our own -- helps us all think critically about investing and make decisions that help us become smarter, happier, and richer.