Composers today are not bound to a tag they are free. Some have serial influences, some focus on rhythm with stravinskian influences, others purely comercial - but in the case of classical 20\21st century many different techniques are employed, and with bespoke combination of instruments.
Serialism has strict rules but many composers today like John Mcleod, take serialistic aspects - like a tone row of a certain number of notes, not always 12 tone, with frequent use of transposition ect but you have to listen to these pieces to truly appreciate them and look through scores to understand them due to the fact that there not easily defined by a catchy tune. Boulez is another composer who loves his serialism
Most composers are heavily influenced by stravinsky - rite of spring / petroushka due to his use of poly-tonality = combining triads e.g in petroushka he uses a C & D chord together in the strings and in the rite of spring he used an E7th and Eb7 on top of each other in the cellos - stravinsky also uses changes in metre changing each bar from 2/8 - 3/4 - 2/4 - 6/8 ect. Composers like Thomas Ades use very complex rhythms and sit for hours trying to work them out - listen to any Ades piece my favourites are America: a prophecy & Asyla - III - ecstacio.
However, if you analyse these pieces you will understand them, which i cant stress enough as Ades's pieces are Atonal yet the chords aren't random if you analyse them - they make perfect sense.
other composers like Mark Anthony-Turnage have heavy influences from jazz, yet still that Stravinskian rhythmic patterns and tonality - for example Scherzoid, sounds nothing like serialism.
There is a lot of music being composed today which like pop music can be followed, and its your own preference if you like it or not! - its not all lumped in and sounds the same
Scriabin's piano sonatas are from the late 1800 - early 1900 (died in 1911) and his works change the texture and rhythm - like later schoenberg and webern - instead of harmony and melody. but he kept a tonal basis except for his later atonal sonatas.
Debussy as well, people often forget, the use of the whole tone scale and pentatonic scale. Debussy and ravel portray images and scenes very well but if you look at the music, the harmony is rather abstract.
Bartok - who took folk tunes - he was font of parallelism, like debussy. - where a chord shifts by exact semi-tone / tone difference.
Commercial modern compositions arent so fantastic - listen to ANY John williams theme tune and they all go I - V in the first bar of the melody. I say this as they are purely commercial - im not criticising as they are great compositions but can't be grouped with classical. On the other hand many horror films are influenced by stravinksy and his rite of spring.
Other composers dont want any definition and compose to 'Portray' something - a picture / smell / feeling. And people forget that your portraying it through another sense which is sound. They cant hear a structure or they look at the score and see no relevance - this is because the only way to notate music is in a tonal way, even if what your writing is atonal.
If you want to get into modern music it may take a while to get to grips. Minimalism i have left out but many composers have influeced from the use of cells - and use this to develop their rhythms
Music Listen to: (<< = important)
Bartok - Music for strings percussion and celesta - I is an atonal fugue. & parallelism in II + III<<
Debussy - Bells between the leaves / fireworks (literally fireworks on the piano) <<
Ravel - String quartet in F + water games
Scriabin - Black mass sonata - atonal
Stravinsky - The Rite of Spring <<
Webern - Quartets - serialism << defines his sections by changing the texture and dynamics
Tippett - Double concerto for strings - uses pentatonic scale
Berio - sequenza's (These are avant garde and i personaly dont like them - this is random music with no structure or relation!)
Ades - Asyla, I - II - III + IV (III is the easiest to follow, he portrays club music through his orchestra) / Tevot / America: A prohecy <<
Turnage - Scherzoid
hope this helps