The ATLAS Liquid Argon (LAr) Calorimeter readout electronics will be upgraded to meet the new trigger and data-acquisition (TDAQ) buffering requirements and to withstand the high expected radiation doses at the high-luminosity LHC. The triangular calorimeter signals are amplified and shaped by analog electronics over a dynamic range of 16 bits, with low noise and excellent linearity. Development of low-power preamplifiers and shapers to meet these requirements in130nm CMOS technology are ongoing. Development of a radiation-hard, low-power, 14-bitpipeline+SAR analog-to-digital converter (ADC) to digitize the analog signals in 65nm CMOS technology is ongoing. Characterization of the prototypes of the front-end components show good promise to fulfill all the requirements. The signals will be sent at 40 MHz to the off-detector electronics, where FPGAs connected through high-speed links will perform energy and time reconstruction through the application of corrections and digital filtering. Reduced data are sent with low latency to the first-level trigger, while the full data are buffered until the reception of trigger accept signals. The data-processing, control and timing functions will be realized by dedicated boards connected through ATCA crates. Results of tests of prototypes of front-end components will be presented, along with design studies on the performance of the off-detector readout system.