'Oppo', you should note, is bundled in with OnePlus and Realme, since they're all part of the giant BBK Group in China. If Oppo phones were broken out (ditto OnePlus, etc.) then their market share would be much smaller. But it's fair to group all these together, since they use many of the same designs and components.
From Trendforce's press release:
Owing to high sales of the iPhone 12 series as well as an aggressive device production strategy by Chinese smartphone brands in response to sanctions on Huawei, which has lost considerable market share as a result, global smartphone production for 1Q21 is likely to reach 342 million units, a YoY increase of 25% and a QoQ decline of just 6%... Historically, smartphone production tends to experience a QoQ drop of around 20% for the first quarter as demand collapses from the peak-season level of the fourth quarter of the preceding year. However, the performance of the first quarter of this year is expected to defy seasonality.
Even though the share of high-end models in global smartphone sales shrank in 2020 due to the COVID-19 pandemic, Apple was able to push through the headwinds and capture market share by introducing 5G models and adopting an aggressive pricing strategy. Apple produced 77.6 million units of iPhones in 4Q20, an 85% increase QoQ, thereby overtaking Samsung and ranking first amongst all smartphone brands. It should also be pointed out that iPhone 12 devices accounted for about 90% of the iPhone production in 4Q20. For 1Q21, sales of iPhone 12 devices remain strong, and total iPhone production is expected to reach 54 million units, with iPhone 12 models again accounting for about 80% of this figure...
...Samsung posted a QoQ decline of 14% in its smartphone production to 67 million units for 4Q20, thereby taking second place in the quarterly ranking. Its performance was affected by the competition from the new iPhone devices and the end of stock-up activities that were related to the year-end holiday season in North America and Europe. Moving to 1Q21, Samsung has released the new lineup of its flagship Galaxy S21 series in advance so as to maintain its market share in the high-end segment. At the same time, Samsung has adopted promotional pricing to boost the sales of its latest devices. Samsung’s quarterly smartphone production volume will likely reach around 62 million units for 1Q21. For the whole 2021, TrendForce expects Samsung to top the annual ranking of brands by production. Nevertheless, retaining the leadership position will be increasingly challenging for Samsung as it has been losing market share to several Chinese brands that have risen rapidly over these past few years...
...OPPO (including OPPO, OnePlus, Realme), Xiaomi, and Vivo produced 50 million, 47 million, and 31.5 million units of smartphones respectively in 4Q20, which placed them at third, fourth, and sixth places. Looking ahead to 1Q21, the three aforementioned smartphone brands are expected to maintain an aggressive production target and actively expand in both the overseas and domestic markets. Nonetheless, potential growths in their actual production volume will be limited by the current shortage of production capacities across the foundry industry. In terms of product strategies, the three Chinese brands will remain aggressive in their R&D activities for high-end models as they seek to take over Huawei’s previous position in this segment. In particular, Xiaomi and OPPO have been seizing market shares with the highly cost-effective Redmi and Realme series, respectively. Notably, Xiaomi is expected to achieve a better performance in terms of market share for the whole year due to its earlier expansion in the overseas markets.
In response to heightened China-U.S. tensions, Huawei maintained a high inventory of components, which allowed it to effectively mitigate the impact of sanctions from the Department of Commerce. As such, Huawei recorded a quarterly production volume of 34.5 million units in 4Q20, a 21% decrease QoQ. This performance was sufficient to land Huawei in the fifth place in the production ranking for the quarter. Going forward, if suppliers of relevant smartphone components are unable to obtain approval to ship to Huawei by the end of 1Q21, then Huawei is expected to experience a noticeable cutoff of material supplies by the end of 2Q21. Furthermore, after being officially sold off by its parent company Huawei in early 2021, Honor is similarly facing the issue of foundry capacity shortage, which is projected to constrain the production volume of new Honor for the entirety of 2021.
Helpfully, the stats are broken into a table (albeit heavily watermarked):
Whether you're looking at Q4 2020 sales or Q1 2021 estimates, the emergence of the 'big four' is obvious, at least with that 'Oppo = BBK Group' caveat. Apple and Samsung have been jockeying for first place for the last half decade and this will continue for the forseeable future. Samsung's phone releases are a lot patchier in design and quality, arguably, than Apple's, but Samsung covers a wider price range and can hit every segment of the market in every country, backed by copious marketing.
Huawei was the main challenger to the 'big two', but the USA/Trump's sactions against the company have really started to hit hard and will get worse before it gets better. Even with China-only sales, Huawei will drop out of the top 6 phone makers before the end of this year. Which is all very sad, since Huawei has made great progess in imaging, in particular, now modelled on smartphones that few people will ever get to try in the Western world.
Of additional note is Xiaomi's rising star. Their 'top tech at ever improving value for money' approach is now mainstream in the West and with new smartphones appearing every month - I last featured a Xiaomi phone here, late last year, but watch this space for more comparisons. With cameras that consistently outperform their raw specs and with stereo speakers, decent displays, and (now) NFC across the board, there's a lot to recommend Xiaomi smartphones, from £200 up through £500.
Of additional note is that the 'new Nokia', i.e. HMD, is not in the top 6 - Nokia's Android handsets have been occasionally innovative and usually solidly made, but also often over-priced for their specs. Also not present now is LG, which is now ninth in the rankings, despite plenty of innovative ideas and a welcome continued concentration on media and durability - LG just hasn't been consistent enough across the board (hardware/software/innovation).
AAWP readers here in search of a new smartphone should perhaps start with (in descending price order) the iPhone 12 Pro range (last featured here), the Samsung S20 FE (last featured here), or any one of a number of £200-ish Xiaomi smartphones (watch for daily and weekly offers, prices fluctuate wildly!)