It's not clear exactly what genres (the phrase "modern music" isn't very precise) you're asking about, so I'll cover several of them:
- Rock, Hard Rock, Punk, Country: More often real acoustic drums played by a drummer and recorded. Sometimes drum replacement may be used if one or more of the drum sounds is off or has a problem - that's where the acoustic recording is used to trigger a sampled drum sound, more common on snares and toms in this genre, but might be used on kick. Punk and Country are more likely to be 100% real drums. One popular thing to do these days is record the whole track acoustic, and then overlay replaced sounds and mix between them for aesthetic reasons. Like the intro might be synth drums triggered by the real drummer and then the first verse it might switch to acoustic drums.
- Metal (all kinds): Usually as above, but for faster drumming, the kick drum is more often replaced (called "triggered" in the metal world). Other drums may be replaced as needed, but drum replacement in all genres can be tricky because drums can sound fake after drum replacement.
- R&B, Pop: Whatever works for the song. Sometimes all acoustic, sometimes synth drums, sometimes sampled and sequenced or triggered, could be a drum machine, could be multiple layers of different kinds of sounds. One aspect of Pop has always been a focus on whatever will make the track a hit in the target market, sometimes even at relatively extravagant cost. So anything and everything is possible.
- Hip-hop, Rap: Most often a drum machine (synth or sampled) or synth or sampled drums sequenced right in the DAW. Timbaland, for example, often lays down a beat box groove with a microphone to get the right feel, and then replace his beat boxing with drum sampled in Ableton Live. This keeps the production costs low and the process fast and also allows the producer/beatmaker more control over the whole beat. It's also the sound of the genre. Often drum sounds, especially kick sounds, are layered up from more than one sound in order to get a full sound with a lot of impact. The "sonics" are critical in this genre. Sampled drum loops might be used in Hip-hop or more often Rap, and sampled loops or beats might be combined with sequenced drum samples or synth based sounds.
- EDM, Dubstep: Generally everything is sequenced in a DAW and mostly built from samples, but digital and analog synths are popular, as are samples of synths.
Overall, it really depends a lot. Analog synths are back, as are analog drum machines. Also, digital synths and drum machines as well as all kinds of sample packs and virtual synth software are widely available and affordable. Beatmaking has invaded almost every genre of music, even Musical Theatre (Hamilton being a notable example). But just because everyone is making beats doesn't mean no one is recording real drums. As sampling and sample libraries have become much higher in quality, the difference between using a real drum or real analog drum synth, and a sample of either of those has really become a matter of taste. Some producers prefer things to be more "real", others have no problem with using 100% samples.